sr!com.femlab.server.ModelFileHeaderD%LtagstLcom/femlab/util/FlStringList;Ltypesq~LvrsntLcom/femlab/util/FlVersion;xpwsrcom.femlab.util.FlVersion%/B =IbuildImajorLdatetLjava/lang/String;Lextq~Lnameq~Lrcsq~L reactionExtq~L reactionNameq~xpwtq~t#COMSOL Reaction Engineering Lab 3.5tat COMSOL 3.5q~ w[t $Name: $t$Date: 2008/12/03 17:02:19 $xur[Ljava.lang.String;V{Gxpt modelinfotxfemtguitfem0tfem1tg3tg4tg6tfem1tfem1.0q~q~tfem24tfem24.0q~q~tfem21tfem21.0q~q~t mfileinfouq~ q~t femstructt guistructq~q~tdrawq~!q~!tgeomtmeshtsolutiontxmeshq~"q~#q~$q~%q~"q~#q~$q~%q~xsrcom.femlab.api.client.ModelInfo^%Ldescrq~LdocURLq~[imaget[Bxpwptpxuq~ t` COMSOL 3.5 a 0 603 $Name: $ $Date: 2008/12/03 17:02:19 $ 1 geom on on off on on on on 0.1 t FlPerpendicularCurrents cartesian {"Az","redAz"} {"x","y","z"} qa {"shlag(2,'Az')"} 4 2 2 on _qa Lag2 static off {"lm1","lm2"} ideal ref 0 {1,1,1,1,1,1,1,1,1,1,1,1} {"flux*(x/L)/mu0","0"} {"0","0"} 0 0 H cont {1,1,1,2,2,2,2,1,2,2,2,2} 1 1 1 {"0","0"} {"0","0"} 1 {"1","0","0","1"} {"1","0","0","1"} epsr 0 0 mur {"flux*(x/L)/mu0","0"} {"0","0"}
{"0","0"} {"0","0"}
{"1/mu0_qa*Bx_qa","1/mu0_qa*By_qa"} {"1/mu0_qa*Bx_qa","1/mu0_qa*By_qa"} 1/mu0_qa*normB_qa 1 0 0 {"0","0"} {"0","0"} 0 1 {1,1,2}
8.854187817e-12 4*pi*1e-7
FlNavierStokes cartesian {"u","v","p","nxw","nyw"} {"x","y","z"} ns {"shlag(2,'u')","shlag(2,'v')","shlag(1,'p')"} 4 2 2 1 2 off _ns Lagp2p1 static Off off {"lm3","lm4","lm5"} ideal ref 0 0 {1,1,1,1,1,1,1,1,1,1,1,1} int walltype inlet outlet uv p p p ntotstress noslip ntotstress totstress cont U0in 0 0 0 0 {"0","0"} {"0","0"} {"0","0"} {"0","0"} 1 1 u_in 1 0 0 0 0 0 {1,1,1,3,2,2,4,1,2,2,2,2} 1 2 3 1 2 3 1 1 2 1 1 2 1 1 2 1 1 2 {"0","0","0","0","0"} {"0","0","0","0","0"} 0 1 1 rho 1 eta 0 mu0*Mv*d(Hx_qa,x) 0 mu0*Mv*d(Hy_qa,y) 0 0.5 1 gls 0.25 1 sc 0.35 0 1 0.1 0 navierstokes usesELM 0 Lagp2p1 0 Lagp2p1 0 0 0 {1,2,1} 10 {"x","y"} {"ref"} {"shlag(2,'Az')","shlag(2,'u')","shlag(2,'v')","shlag(1,'p')"} 4 2 2 1 2 on 1
general
SI {"0","0","0","0"} 1 1 1 2 {1,1,1} 1 1 2 3 4 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"dVol_qa*(Jz_qa*test(depAz_qa)-Hx_qa*test(curlAx_qa)-Hy_qa*test(curlAy_qa))","0","0","0"} {"dVol_qa*(Jz_qa*test(depAz_qa)-Hx_qa*test(curlAx_qa)-Hy_qa*test(curlAy_qa))","gls_ns+shock_capt_ns","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"-d(-2*eta_ns*ux+p,Azx)","-d(-eta_ns*(uy+vx),Azx)","-d(-2*eta_ns*ux+p,Azy)","-d(-eta_ns*(uy+vx),Azy)"} {"-d(-eta_ns*(vx+uy),Azx)","-d(-2*eta_ns*vy+p,Azx)","-d(-eta_ns*(vx+uy),Azy)","-d(-2*eta_ns*vy+p,Azy)"} {"0"} {"0"} {"-d(-2*eta_ns*ux+p,ux)","-d(-eta_ns*(uy+vx),ux)","-d(-2*eta_ns*ux+p,uy)","-d(-eta_ns*(uy+vx),uy)"} {"-d(-eta_ns*(vx+uy),ux)","-d(-2*eta_ns*vy+p,ux)","-d(-eta_ns*(vx+uy),uy)","-d(-2*eta_ns*vy+p,uy)"} {"0"} {"0"} {"-d(-2*eta_ns*ux+p,vx)","-d(-eta_ns*(uy+vx),vx)","-d(-2*eta_ns*ux+p,vy)","-d(-eta_ns*(uy+vx),vy)"} {"-d(-eta_ns*(vx+uy),vx)","-d(-2*eta_ns*vy+p,vx)","-d(-eta_ns*(vx+uy),vy)","-d(-2*eta_ns*vy+p,vy)"} {"0"} {"0"} {"-d(-2*eta_ns*ux+p,px)","-d(-eta_ns*(uy+vx),px)","-d(-2*eta_ns*ux+p,py)","-d(-eta_ns*(uy+vx),py)"} {"-d(-eta_ns*(vx+uy),px)","-d(-2*eta_ns*vy+p,px)","-d(-eta_ns*(vx+uy),py)","-d(-2*eta_ns*vy+p,py)"} {"0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","-d(F_x_ns-rho_ns*(u*ux+v*uy),Az)","-d(F_y_ns-rho_ns*(u*vx+v*vy),Az)","-d(-divU_ns,Az)","0","-d(F_x_ns-rho_ns*(u*ux+v*uy),u)","-d(F_y_ns-rho_ns*(u*vx+v*vy),u)","-d(-divU_ns,u)","0","-d(F_x_ns-rho_ns*(u*ux+v*uy),v)","-d(F_y_ns-rho_ns*(u*vx+v*vy),v)","-d(-divU_ns,v)","0","-d(F_x_ns-rho_ns*(u*ux+v*uy),p)","-d(F_y_ns-rho_ns*(u*vx+v*vy),p)","-d(-divU_ns,p)"} {"0","0","0","0"} {"0","F_x_ns-rho_ns*(u*ux+v*uy)","F_y_ns-rho_ns*(u*vx+v*vy)","-divU_ns"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"-d(-2*eta_ns*ux+p,Az)","-d(-eta_ns*(uy+vx),Az)"} {"-d(-eta_ns*(vx+uy),Az)","-d(-2*eta_ns*vy+p,Az)"} {"0","0"} {"0","0"} {"-d(-2*eta_ns*ux+p,u)","-d(-eta_ns*(uy+vx),u)"} {"-d(-eta_ns*(vx+uy),u)","-d(-2*eta_ns*vy+p,u)"} {"0","0"} {"0","0"} {"-d(-2*eta_ns*ux+p,v)","-d(-eta_ns*(uy+vx),v)"} {"-d(-eta_ns*(vx+uy),v)","-d(-2*eta_ns*vy+p,v)"} {"0","0"} {"0","0"} {"-d(-2*eta_ns*ux+p,p)","-d(-eta_ns*(uy+vx),p)"} {"-d(-eta_ns*(vx+uy),p)","-d(-2*eta_ns*vy+p,p)"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"-d(F_x_ns-rho_ns*(u*ux+v*uy),Azx)","-d(F_x_ns-rho_ns*(u*ux+v*uy),Azy)"} {"-d(F_y_ns-rho_ns*(u*vx+v*vy),Azx)","-d(F_y_ns-rho_ns*(u*vx+v*vy),Azy)"} {"-d(-divU_ns,Azx)","-d(-divU_ns,Azy)"} {"0","0"} {"-d(F_x_ns-rho_ns*(u*ux+v*uy),ux)","-d(F_x_ns-rho_ns*(u*ux+v*uy),uy)"} {"-d(F_y_ns-rho_ns*(u*vx+v*vy),ux)","-d(F_y_ns-rho_ns*(u*vx+v*vy),uy)"} {"-d(-divU_ns,ux)","-d(-divU_ns,uy)"} {"0","0"} {"-d(F_x_ns-rho_ns*(u*ux+v*uy),vx)","-d(F_x_ns-rho_ns*(u*ux+v*uy),vy)"} {"-d(F_y_ns-rho_ns*(u*vx+v*vy),vx)","-d(F_y_ns-rho_ns*(u*vx+v*vy),vy)"} {"-d(-divU_ns,vx)","-d(-divU_ns,vy)"} {"0","0"} {"-d(F_x_ns-rho_ns*(u*ux+v*uy),px)","-d(F_x_ns-rho_ns*(u*ux+v*uy),py)"} {"-d(F_y_ns-rho_ns*(u*vx+v*vy),px)","-d(F_y_ns-rho_ns*(u*vx+v*vy),py)"} {"-d(-divU_ns,px)","-d(-divU_ns,py)"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"-2*eta_ns*ux+p","-eta_ns*(uy+vx)"} {"-eta_ns*(vx+uy)","-2*eta_ns*vy+p"} {"0","0"} 1 1 1 1 1 1 1 1 1 {"Az","u","v","p"} Azy -Azx 1 curlAx_qa curlAy_qa Bx_qa/(mur_qa*mu0_qa) By_qa/(mur_qa*mu0_qa) mu0_qa*mur_qa mu0_qa*murxx_qa mu0_qa*murxy_qa mu0_qa*muryx_qa mu0_qa*muryy_qa sigma_qa*deltaV_qa/L_qa Jpz_qa+Jvz_qa+Jez_qa Jz_qa*(vx_qa*By_qa-vy_qa*Bx_qa+deltaV_qa/L_qa) Wm_qa dVol_qa*W_qa 0.5*(Hx_qa*Bx_qa+Hy_qa*By_qa) -Jz_qa*By_qa Jz_qa*Bx_qa sqrt(abs(FLtzx_qa)^2+abs(FLtzy_qa)^2) sqrt(abs(Mx_qa)^2+abs(My_qa)^2) sqrt(abs(Brx_qa)^2+abs(Bry_qa)^2) sqrt(abs(Hx_qa)^2+abs(Hy_qa)^2) sqrt(abs(Bx_qa)^2+abs(By_qa)^2) abs(Jz_qa) sigma_qa*Evz_qa vx_qa*By_qa-vy_qa*Bx_qa abs(Evz_qa) sqrt(abs(vx_qa)^2+abs(vy_qa)^2) sqrt(u^2+v^2) vx-uy ux+vy rho_ns*U_ns*h/eta_ns rho_ns*(u*ux+v*uy)+px-F_x_ns-eta_ns*(2*uxx+uyy+vxy) rho_ns*(u*vx+v*vy)+py-F_y_ns-eta_ns*(vxx+uyx+2*vyy) rho_ns*u rho_ns*v eta_ns rho_ns nojac(1/max(2*rho_ns*sqrt(emetric(u,v)),48*eta_ns/h^2)) 0.5*nojac(if(u^2+v^2<sqrt(eps),h*U_ref_ns,(u^2+v^2)/sqrt(emetric(u,v)))) rho_ns*divU_ns 0 0 normB_qa/mu0_qa 1 0 0 0 1 Az murxx_qa Bx_qa/mu0_qa-Hx_qa 0 By_qa/mu0_qa-Hy_qa 0 1 0 0 1 1/mur_qa 0 0 1/mur_qa 0 0 rho eta mu0*Mv*d(Hx_qa,x) mu0*Mv*d(Hy_qa,y) 0.5 0.25 sc 0.35 1 0.1 0 Lagp2p1 Lagp2p1 -test(nojac(rho_ns)*(nojac(u)*ux+nojac(v)*uy)+px-nojac(eta_ns)*(2*uxx+uyy+vxy))*taum_ns*res_u_ns-test(nojac(rho_ns)*(nojac(u)*vx+nojac(v)*vy)+py-nojac(eta_ns)*(vxx+uyx+2*vyy))*taum_ns*res_v_ns-test(divU_ns)*tauc_ns*res_p_ns 0 (d(x,xi1)^2+d(x,xi2)^2)^2+2*(d(y,xi1)*d(x,xi1)+d(y,xi2)*d(x,xi2))^2+(d(y,xi1)^2+d(y,xi2)^2)^2 U_ns d(x,xi1)^2+d(x,xi2)^2 d(y,xi1)*d(x,xi1)+d(y,xi2)*d(x,xi2) d(y,xi1)^2+d(y,xi2)^2 -nojac(0.5*min(ck_ns*sqrt((tauc_ns*res_p_ns/(nojac(rhoint_g1_ns/vol_g1_ns)*nojac(sqrt(u2int_g1_ns/vol_g1_ns))))^2+(taum_ns*res_u_ns)^2+(taum_ns*res_v_ns)^2),U_ref_ns)*min(gijgij_ns^(-0.25),rho_ns*U_ref_ns/(48*eta_ns)))*rho_ns*(g11_ns*(ux*test(ux)+vx*test(vx))+g21_ns*(uy*test(ux)+vy*test(vx))+g21_ns*(ux*test(uy)+vx*test(vy))+g22_ns*(uy*test(uy)+vy*test(vy))) {0,0,0} {0,0,0} {1,2,1} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","-u-U0in_ns*nx_ns","-v-U0in_ns*ny_ns","0"} {"0","-u","-v","0"} {"0","-u","-v","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","test(-u-U0in_ns*nx_ns)","test(-v-U0in_ns*ny_ns)","0"} {"0","test(-u)","test(-v)","0"} {"0","test(-u)","test(-v)","0"} {"0","0","0","0"} {"-d(dVolbnd_qa*ny_qa*H0x_qa,Az)","0","0","0","-d(dVolbnd_qa*ny_qa*H0x_qa,u)","0","0","0","-d(dVolbnd_qa*ny_qa*H0x_qa,v)","0","0","0","-d(dVolbnd_qa*ny_qa*H0x_qa,p)","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"dVolbnd_qa*ny_qa*H0x_qa","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} 1 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 {"","","",""} {"","","",""} {"","","",""} {"","","",""} {"","","",""} {"","","",""} {"","","",""} {"","","",""} {"","","",""} {"","","",""} {"Az","u","v","p"} 1 unx*(Hy_qa_down-Hy_qa_up)-uny*(Hx_qa_down-Hx_qa_up) -0.5*(Bx_qa_up*Hx_qa_up+By_qa_up*Hy_qa_up)*dnx+(dnx*Hx_qa_up+dny*Hy_qa_up)*Bx_qa_up -0.5*(Bx_qa_down*Hx_qa_down+By_qa_down*Hy_qa_down)*unx+(unx*Hx_qa_down+uny*Hy_qa_down)*Bx_qa_down -0.5*(Bx_qa_up*Hx_qa_up+By_qa_up*Hy_qa_up)*dny+(dnx*Hx_qa_up+dny*Hy_qa_up)*By_qa_up -0.5*(Bx_qa_down*Hx_qa_down+By_qa_down*Hy_qa_down)*uny+(unx*Hx_qa_down+uny*Hy_qa_down)*By_qa_down -Jsz_qa*By_qa Jsz_qa*Bx_qa sqrt(abs(FsLtzx_qa)^2+abs(FsLtzy_qa)^2) eta_ns*(2*nx_ns*ux+ny_ns*(uy+vx)) eta_ns*(2*nx_ns*ux+ny_ns*(uy+vx)) eta_ns*(2*nx_ns*ux+ny_ns*(uy+vx)) eta_ns*(2*nx_ns*ux+ny_ns*(uy+vx)) -nx_ns*p+2*nx_ns*eta_ns*ux+ny_ns*eta_ns*(uy+vx) -nx_ns*p+2*nx_ns*eta_ns*ux+ny_ns*eta_ns*(uy+vx) -nx_ns*p+2*nx_ns*eta_ns*ux+ny_ns*eta_ns*(uy+vx) -nx_ns*p+2*nx_ns*eta_ns*ux+ny_ns*eta_ns*(uy+vx) eta_ns*(nx_ns*(vx+uy)+2*ny_ns*vy) eta_ns*(nx_ns*(vx+uy)+2*ny_ns*vy) eta_ns*(nx_ns*(vx+uy)+2*ny_ns*vy) eta_ns*(nx_ns*(vx+uy)+2*ny_ns*vy) -ny_ns*p+nx_ns*eta_ns*(vx+uy)+2*ny_ns*eta_ns*vy -ny_ns*p+nx_ns*eta_ns*(vx+uy)+2*ny_ns*eta_ns*vy -ny_ns*p+nx_ns*eta_ns*(vx+uy)+2*ny_ns*eta_ns*vy -ny_ns*p+nx_ns*eta_ns*(vx+uy)+2*ny_ns*eta_ns*vy 0 0 nx ny flux*x/(L*mu0) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 u_in 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 dnx unx dnx unx dny uny dny uny 0 0 0 0 0 0 0 0 {0,0,0,0,0,0,0,0,0,0,0,0} {0,0,0,0,0,0,0,0,0,0,0,0} {1,1,1,2,3,4,5,1,4,3,4,3} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} 1 1 2 3 4 1 1 1 1 1 1 1 1 1 {"","","",""} {"","","",""t`} {"","","",""} {"","","",""} {"Az","u","v","p"} 0 0 {0,0,0,0,0,0,0,0,0,0,0,0} {0,0,0,0,0,0,0,0,0,0,0,0} {1,1,2,2,2,2,2,2,2,2,1,1} 8.854187817000001e-012 4e-007*pi 10 elcplscalar {"1"} nojac(rho_ns) nojac(1) nojac(max((+(u)^2+(v)^2),(eta_ns/rho_ns/h)^2)) nojac(-1/max(emetric(u,v),(visc_vel_fact_ns*eta_ns/rho_ns)^2*emetric2)) ref ref ref ref ref ref ref ref 0 0 0 0 0 0 0 0 {"1","3"} {"2"} {"rhoint_g1_ns","vol_g1_ns","u2int_g1_ns","mdt2_cfl_g1_ns"} {"1","2","3","4"} {"4"} elconst nojac(sqrt(-mdt2_cfl_g1_ns))

{"E1","R1","R2"} 4*pi*1e-7 [Wb/A/m] 0.001 [Pa*s] 5e-9 [m] 1/6/pi/eta/a 55*5.15*1000 [A/m] 4*pi*a^3/3 96500[C/mol] 1e16 [mol/m^3] 1.4e-3 [m] 1.3 [Wb/m^2] 0.05e-4[m] 0.005e-4[m] 1e-6 [m/s] 0 [m/s] 1.38e-23 [J/K] 298 [K] 1000 [kg/m^3] Mv maximum Satn M a radius {0} {0} qa weak SI COMSOL 3.5 a 0 603 $Name: $ $Date: 2008/12/03 17:02:19 $ 1 geom on on off on on on on 0.1 t FlPerpendicularCurrents cartesian {"Az","redAz"} {"x","y","z"} qa {"shlag(2,'Az')"} 4 2 2 on _qa Lag2 static off {"lm1","lm2"} ideal ref 0 {1,1,1,1,1,1,1,1,1,1,1,1} {"flux*(x/L)/mu0","0"} {"0","0"} 0 0 H cont {1,1,1,2,2,2,2,1,2,2,2,2} 1 1 1 {"0","0"} {"0","0"} 1 {"1","0","0","1"} {"1","0","0","1"} epsr 0 0 mur {"flux*(x/L)/mu0","0"} {"0","0"}
{"0","0"} {"0","0"}
{"1/mu0_qa*Bx_qa","1/mu0_qa*By_qa"} {"1/mu0_qa*Bx_qa","1/mu0_qa*By_qa"} 1/mu0_qa*normB_qa 1 0 0 {"0","0"} {"0","0"} 0 1 {1,1,2}
8.854187817e-12 4*pi*1e-7
FlNavierStokes cartesian {"u","v","p","nxw","nyw"} {"x","y","z"} ns {"shlag(2,'u')","shlag(2,'v')","shlag(1,'p')"} 4 2 2 1 2 off _ns Lagp2p1 static Off off {"lm3","lm4","lm5"} ideal ref 0 0 {1,1,1,1,1,1,1,1,1,1,1,1} int walltype inlet outlet uv p p p ntotstress noslip ntotstress totstress cont U0in 0 0 0 0 {"0","0"} {"0","0"} {"0","0"} {"0","0"} 1 1 u_in 1 0 0 0 0 0 {1,1,1,3,2,2,4,1,2,2,2,2} 1 2 3 1 2 3 1 1 2 1 1 2 1 1 2 1 1 2 {"0","0","0","0","0"} {"0","0","0","0","0"} 0 1 1 rho 1 eta 0 mu0*Mv*d(Hx_qa,x) 0 mu0*Mv*d(Hy_qa,y) 0 0.5 1 gls 0.25 1 sc 0.35 0 1 0.1 0 navierstokes usesELM 0 Lagp2p1 0 Lagp2p1 0 0 0 {1,2,1} 10 {"x","y"} {"ref"} {"shlag(2,'Az')","shlag(2,'u')","shlag(2,'v')","shlag(1,'p')"} 4 2 2 1 2 on 1
general
SI {"0","0","0","0"} 1 1 1 2 {1,1,1} 1 1 2 3 4 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"dVol_qa*(Jz_qa*test(depAz_qa)-Hx_qa*test(curlAx_qa)-Hy_qa*test(curlAy_qa))","0","0","0"} {"dVol_qa*(Jz_qa*test(depAz_qa)-Hx_qa*test(curlAx_qa)-Hy_qa*test(curlAy_qa))","gls_ns+shock_capt_ns","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"-d(-2*eta_ns*ux+p,Azx)","-d(-eta_ns*(uy+vx),Azx)","-d(-2*eta_ns*ux+p,Azy)","-d(-eta_ns*(uy+vx),Azy)"} {"-d(-eta_ns*(vx+uy),Azx)","-d(-2*eta_ns*vy+p,Azx)","-d(-eta_ns*(vx+uy),Azy)","-d(-2*eta_ns*vy+p,Azy)"} {"0"} {"0"} {"-d(-2*eta_ns*ux+p,ux)","-d(-eta_ns*(uy+vx),ux)","-d(-2*eta_ns*ux+p,uy)","-d(-eta_ns*(uy+vx),uy)"} {"-d(-eta_ns*(vx+uy),ux)","-d(-2*eta_ns*vy+p,ux)","-d(-eta_ns*(vx+uy),uy)","-d(-2*eta_ns*vy+p,uy)"} {"0"} {"0"} {"-d(-2*eta_ns*ux+p,vx)","-d(-eta_ns*(uy+vx),vx)","-d(-2*eta_ns*ux+p,vy)","-d(-eta_ns*(uy+vx),vy)"} {"-d(-eta_ns*(vx+uy),vx)","-d(-2*eta_ns*vy+p,vx)","-d(-eta_ns*(vx+uy),vy)","-d(-2*eta_ns*vy+p,vy)"} {"0"} {"0"} {"-d(-2*eta_ns*ux+p,px)","-d(-eta_ns*(uy+vx),px)","-d(-2*eta_ns*ux+p,py)","-d(-eta_ns*(uy+vx),py)"} {"-d(-eta_ns*(vx+uy),px)","-d(-2*eta_ns*vy+p,px)","-d(-eta_ns*(vx+uy),py)","-d(-2*eta_ns*vy+p,py)"} {"0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","-d(F_x_ns-rho_ns*(u*ux+v*uy),Az)","-d(F_y_ns-rho_ns*(u*vx+v*vy),Az)","-d(-divU_ns,Az)","0","-d(F_x_ns-rho_ns*(u*ux+v*uy),u)","-d(F_y_ns-rho_ns*(u*vx+v*vy),u)","-d(-divU_ns,u)","0","-d(F_x_ns-rho_ns*(u*ux+v*uy),v)","-d(F_y_ns-rho_ns*(u*vx+v*vy),v)","-d(-divU_ns,v)","0","-d(F_x_ns-rho_ns*(u*ux+v*uy),p)","-d(F_y_ns-rho_ns*(u*vx+v*vy),p)","-d(-divU_ns,p)"} {"0","0","0","0"} {"0","F_x_ns-rho_ns*(u*ux+v*uy)","F_y_ns-rho_ns*(u*vx+v*vy)","-divU_ns"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"-d(-2*eta_ns*ux+p,Az)","-d(-eta_ns*(uy+vx),Az)"} {"-d(-eta_ns*(vx+uy),Az)","-d(-2*eta_ns*vy+p,Az)"} {"0","0"} {"0","0"} {"-d(-2*eta_ns*ux+p,u)","-d(-eta_ns*(uy+vx),u)"} {"-d(-eta_ns*(vx+uy),u)","-d(-2*eta_ns*vy+p,u)"} {"0","0"} {"0","0"} {"-d(-2*eta_ns*ux+p,v)","-d(-eta_ns*(uy+vx),v)"} {"-d(-eta_ns*(vx+uy),v)","-d(-2*eta_ns*vy+p,v)"} {"0","0"} {"0","0"} {"-d(-2*eta_ns*ux+p,p)","-d(-eta_ns*(uy+vx),p)"} {"-d(-eta_ns*(vx+uy),p)","-d(-2*eta_ns*vy+p,p)"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"-d(F_x_ns-rho_ns*(u*ux+v*uy),Azx)","-d(F_x_ns-rho_ns*(u*ux+v*uy),Azy)"} {"-d(F_y_ns-rho_ns*(u*vx+v*vy),Azx)","-d(F_y_ns-rho_ns*(u*vx+v*vy),Azy)"} {"-d(-divU_ns,Azx)","-d(-divU_ns,Azy)"} {"0","0"} {"-d(F_x_ns-rho_ns*(u*ux+v*uy),ux)","-d(F_x_ns-rho_ns*(u*ux+v*uy),uy)"} {"-d(F_y_ns-rho_ns*(u*vx+v*vy),ux)","-d(F_y_ns-rho_ns*(u*vx+v*vy),uy)"} {"-d(-divU_ns,ux)","-d(-divU_ns,uy)"} {"0","0"} {"-d(F_x_ns-rho_ns*(u*ux+v*uy),vx)","-d(F_x_ns-rho_ns*(u*ux+v*uy),vy)"} {"-d(F_y_ns-rho_ns*(u*vx+v*vy),vx)","-d(F_y_ns-rho_ns*(u*vx+v*vy),vy)"} {"-d(-divU_ns,vx)","-d(-divU_ns,vy)"} {"0","0"} {"-d(F_x_ns-rho_ns*(u*ux+v*uy),px)","-d(F_x_ns-rho_ns*(u*ux+v*uy),py)"} {"-d(F_y_ns-rho_ns*(u*vx+v*vy),px)","-d(F_y_ns-rho_ns*(u*vx+v*vy),py)"} {"-d(-divU_ns,px)","-d(-divU_ns,py)"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"-2*eta_ns*ux+p","-eta_ns*(uy+vx)"} {"-eta_ns*(vx+uy)","-2*eta_ns*vy+p"} {"0","0"} 1 1 1 1 1 1 1 1 1 {"Az","u","v","p"} Azy -Azx 1 curlAx_qa curlAy_qa Bx_qa/(mur_qa*mu0_qa) By_qa/(mur_qa*mu0_qa) mu0_qa*mur_qa mu0_qa*murxx_qa mu0_qa*murxy_qa mu0_qa*muryx_qa mu0_qa*muryy_qa sigma_qa*deltaV_qa/L_qa Jpz_qa+Jvz_qa+Jez_qa Jz_qa*(vx_qa*By_qa-vy_qa*Bx_qa+deltaV_qa/L_qa) Wm_qa dVol_qa*W_qa 0.5*(Hx_qa*Bx_qa+Hy_qa*By_qa) -Jz_qa*By_qa Jz_qa*Bx_qa sqrt(abs(FLtzx_qa)^2+abs(FLtzy_qa)^2) sqrt(abs(Mx_qa)^2+abs(My_qa)^2) sqrt(abs(Brx_qa)^2+abs(Bry_qa)^2) sqrt(abs(Hx_qa)^2+abs(Hy_qa)^2) sqrt(abs(Bx_qa)^2+abs(By_qa)^2) abs(Jz_qa) sigma_qa*Evz_qa vx_qa*By_qa-vy_qa*Bx_qa abs(Evz_qa) sqrt(abs(vx_qa)^2+abs(vy_qa)^2) sqrt(u^2+v^2) vx-uy ux+vy rho_ns*U_ns*h/eta_ns rho_ns*(u*ux+v*uy)+px-F_x_ns-eta_ns*(2*uxx+uyy+vxy) rho_ns*(u*vx+v*vy)+py-F_y_ns-eta_ns*(vxx+uyx+2*vyy) rho_ns*u rho_ns*v eta_ns rho_ns nojac(1/max(2*rho_ns*sqrt(emetric(u,v)),48*eta_ns/h^2)) 0.5*nojac(if(u^2+v^2<sqrt(eps),h*U_ref_ns,(u^2+v^2)/sqrt(emetric(u,v)))) rho_ns*divU_ns 0 0 normB_qa/mu0_qa 1 0 0 0 1 Az murxx_qa Bx_qa/mu0_qa-Hx_qa 0 By_qa/mu0_qa-Hy_qa 0 1 0 0 1 1/mur_qa 0 0 1/mur_qa 0 0 rho eta mu0*Mv*d(Hx_qa,x) mu0*Mv*d(Hy_qa,y) 0.5 0.25 sc 0.35 1 0.1 0 Lagp2p1 Lagp2p1 -test(nojac(rho_ns)*(nojac(u)*ux+nojac(v)*uy)+px-nojac(eta_ns)*(2*uxx+uyy+vxy))*taum_ns*res_u_ns-test(nojac(rho_ns)*(nojac(u)*vx+nojac(v)*vy)+py-nojac(eta_ns)*(vxx+uyx+2*vyy))*taum_ns*res_v_ns-test(divU_ns)*tauc_ns*res_p_ns 0 (d(x,xi1)^2+d(x,xi2)^2)^2+2*(d(y,xi1)*d(x,xi1)+d(y,xi2)*d(x,xi2))^2+(d(y,xi1)^2+d(y,xi2)^2)^2 U_ns d(x,xi1)^2+d(x,xi2)^2 d(y,xi1)*d(x,xi1)+d(y,xi2)*d(x,xi2) d(y,xi1)^2+d(y,xi2)^2 -nojac(0.5*min(ck_ns*sqrt((tauc_ns*res_p_ns/(nojac(rhoint_g1_ns/vol_g1_ns)*nojac(sqrt(u2int_g1_ns/vol_g1_ns))))^2+(taum_ns*res_u_ns)^2+(taum_ns*res_v_ns)^2),U_ref_ns)*min(gijgij_ns^(-0.25),rho_ns*U_ref_ns/(48*eta_ns)))*rho_ns*(g11_ns*(ux*test(ux)+vx*test(vx))+g21_ns*(uy*test(ux)+vy*test(vx))+g21_ns*(ux*test(uy)+vx*test(vy))+g22_ns*(uy*test(uy)+vy*test(vy))) {0,0,0} {0,0,0} {1,2,1} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","-u-U0in_ns*nx_ns","-v-U0in_ns*ny_ns","0"} {"0","-u","-v","0"} {"0","-u","-v","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","test(-u-U0in_ns*nx_ns)","test(-v-U0in_ns*ny_ns)","0"} {"0","test(-u)","test(-v)","0"} {"0","test(-u)","test(-v)","0"} {"0","0","0","0"} {"-d(dVolbnd_qa*ny_qa*H0x_qa,Az)","0","0","0","-d(dVolbnd_qa*ny_qa*H0x_qa,u)","0","0","0","-d(dVolbnd_qa*ny_qa*H0x_qa,v)","0","0","0","-d(dVolbnd_qa*ny_qa*H0x_qa,p)","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"dVolbnd_qa*ny_qa*H0x_qa","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} 1 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 {"","","",""} {"","","",""} {"","","",""} {"","","",""} {"","","",""} {"","","",""} {"","","",""} {"","","",""} {"","","",""} {"","","",""} {"Az","u","v","p"} 1 unx*(Hy_qa_down-Hy_qa_up)-uny*(Hx_qa_down-Hx_qa_up) -0.5*(Bx_qa_up*Hx_qa_up+By_qa_up*Hy_qa_up)*dnx+(dnx*Hx_qa_up+dny*Hy_qa_up)*Bx_qa_up -0.5*(Bx_qa_down*Hx_qa_down+By_qa_down*Hy_qa_down)*unx+(unx*Hx_qa_down+uny*Hy_qa_down)*Bx_qa_down -0.5*(Bx_qa_up*Hx_qa_up+By_qa_up*Hy_qa_up)*dny+(dnx*Hx_qa_up+dny*Hy_qa_up)*By_qa_up -0.5*(Bx_qa_down*Hx_qa_down+By_qa_down*Hy_qa_down)*uny+(unx*Hx_qa_down+uny*Hy_qa_down)*By_qa_down -Jsz_qa*By_qa Jsz_qa*Bx_qa sqrt(abs(FsLtzx_qa)^2+abs(FsLtzy_qa)^2) eta_ns*(2*nx_ns*ux+ny_ns*(uy+vx)) eta_ns*(2*nx_ns*ux+ny_ns*(uy+vx)) eta_ns*(2*nx_ns*ux+ny_ns*(uy+vx)) eta_ns*(2*nx_ns*ux+ny_ns*(uy+vx)) -nx_ns*p+2*nx_ns*eta_ns*ux+ny_ns*eta_ns*(uy+vx) -nx_ns*p+2*nx_ns*eta_ns*ux+ny_ns*eta_ns*(uy+vx) -nx_ns*p+2*nx_ns*eta_ns*ux+ny_ns*eta_ns*(uy+vx) -nx_ns*p+2*nx_ns*eta_ns*ux+ny_ns*eta_ns*(uy+vx) eta_ns*(nx_ns*(vx+uy)+2*ny_ns*vy) eta_ns*(nx_ns*(vx+uy)+2*ny_ns*vy) eta_ns*(nx_ns*(vx+uy)+2*ny_ns*vy) eta_ns*(nx_ns*(vx+uy)+2*ny_ns*vy) -ny_ns*p+nxt`_ns*eta_ns*(vx+uy)+2*ny_ns*eta_ns*vy -ny_ns*p+nx_ns*eta_ns*(vx+uy)+2*ny_ns*eta_ns*vy -ny_ns*p+nx_ns*eta_ns*(vx+uy)+2*ny_ns*eta_ns*vy -ny_ns*p+nx_ns*eta_ns*(vx+uy)+2*ny_ns*eta_ns*vy 0 0 nx ny flux*x/(L*mu0) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 u_in 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 dnx unx dnx unx dny uny dny uny 0 0 0 0 0 0 0 0 {0,0,0,0,0,0,0,0,0,0,0,0} {0,0,0,0,0,0,0,0,0,0,0,0} {1,1,1,2,3,4,5,1,4,3,4,3} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} 1 1 2 3 4 1 1 1 1 1 1 1 1 1 {"","","",""} {"","","",""} {"","","",""} {"","","",""} {"Az","u","v","p"} 0 0 {0,0,0,0,0,0,0,0,0,0,0,0} {0,0,0,0,0,0,0,0,0,0,0,0} {1,1,2,2,2,2,2,2,2,2,1,1} 8.854187817000001e-012 4e-007*pi 10 elcplscalar {"1"} nojac(rho_ns) nojac(1) nojac(max((+(u)^2+(v)^2),(eta_ns/rho_ns/h)^2)) nojac(-1/max(emetric(u,v),(visc_vel_fact_ns*eta_ns/rho_ns)^2*emetric2)) ref ref ref ref ref ref ref ref 0 0 0 0 0 0 0 0 {"1","3"} {"2"} {"rhoint_g1_ns","vol_g1_ns","u2int_g1_ns","mdt2_cfl_g1_ns"} {"1","2","3","4"} {"4"} elconst nojac(sqrt(-mdt2_cfl_g1_ns))

4*pi*1e-7 [Wb/A/m] 0.001 [Pa*s] 5e-9 [m] 1/6/pi/eta/a 55*5.15*1000 [A/m] 4*pi*a^3/3 96500[C/mol] 1e16 [mol/m^3] 1.4e-3 [m] 1.3 [Wb/m^2] 0.05e-4[m] 0.005e-4[m] 1e-6 [m/s] 0 [m/s] 1.38e-23 [J/K] 298 [K] 1000 [kg/m^3] Mv maximum Satn M a radius {0} {0} qa weak SI COMSOL 3.5 a 0 603 $Name: $ $Date: 2008/12/03 17:02:19 $ 1 geom on on off on on on on 0.1 t FlPerpendicularCurrents cartesian {"Az","redAz"} {"x","y","z"} qa {"shlag(2,'Az')"} 4 2 2 on _qa Lag2 static off {"lm1","lm2"} ideal ref 0 {1,1,1,1,1,1,1,1,1,1,1,1} {"flux*(x/L)/mu0","0"} {"0","0"} 0 0 H cont {1,1,1,2,2,2,2,1,2,2,2,2} 1 1 1 {"0","0"} {"0","0"} 1 {"1","0","0","1"} {"1","0","0","1"} epsr 0 0 mur {"flux*(x/L)/mu0","0"} {"0","0"}
{"0","0"} {"0","0"}
{"1/mu0_qa*Bx_qa","1/mu0_qa*By_qa"} {"1/mu0_qa*Bx_qa","1/mu0_qa*By_qa"} 1/mu0_qa*normB_qa 1 0 0 {"0","0"} {"0","0"} 0 1 {1,1,2}
8.854187817e-12 4*pi*1e-7
FlNavierStokes cartesian {"u","v","p","nxw","nyw"} {"x","y","z"} ns {"shlag(2,'u')","shlag(2,'v')","shlag(1,'p')"} 4 2 2 1 2 off _ns Lagp2p1 static Off off {"lm3","lm4","lm5"} ideal ref 0 0 {1,1,1,1,1,1,1,1,1,1,1,1} int walltype inlet outlet uv p p p ntotstress noslip ntotstress totstress cont U0in 0 0 0 0 {"0","0"} {"0","0"} {"0","0"} {"0","0"} 1 1 u_in 1 0 0 0 0 0 {1,1,1,3,2,2,4,1,2,2,2,2} 1 2 3 1 2 3 1 1 2 1 1 2 1 1 2 1 1 2 {"0","0","0","0","0"} {"0","0","0","0","0"} 0 1 1 rho 1 eta 0 mu0*Mv*d(Hx_qa,x) 0 mu0*Mv*d(Hy_qa,y) 0 0.5 1 gls 0.25 1 sc 0.35 0 1 0.1 0 navierstokes usesELM 0 Lagp2p1 0 Lagp2p1 0 0 0 {1,2,1} 10 {"x","y"} {"ref"} {"shlag(2,'Az')","shlag(2,'u')","shlag(2,'v')","shlag(1,'p')"} 4 2 2 1 2 on 1
general
SI {"0","0","0","0"} 1 1 1 2 {1,1,1} 1 1 2 3 4 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"dVol_qa*(Jz_qa*test(depAz_qa)-Hx_qa*test(curlAx_qa)-Hy_qa*test(curlAy_qa))","0","0","0"} {"dVol_qa*(Jz_qa*test(depAz_qa)-Hx_qa*test(curlAx_qa)-Hy_qa*test(curlAy_qa))","gls_ns+shock_capt_ns","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"0"} {"-d(-2*eta_ns*ux+p,Azx)","-d(-eta_ns*(uy+vx),Azx)","-d(-2*eta_ns*ux+p,Azy)","-d(-eta_ns*(uy+vx),Azy)"} {"-d(-eta_ns*(vx+uy),Azx)","-d(-2*eta_ns*vy+p,Azx)","-d(-eta_ns*(vx+uy),Azy)","-d(-2*eta_ns*vy+p,Azy)"} {"0"} {"0"} {"-d(-2*eta_ns*ux+p,ux)","-d(-eta_ns*(uy+vx),ux)","-d(-2*eta_ns*ux+p,uy)","-d(-eta_ns*(uy+vx),uy)"} {"-d(-eta_ns*(vx+uy),ux)","-d(-2*eta_ns*vy+p,ux)","-d(-eta_ns*(vx+uy),uy)","-d(-2*eta_ns*vy+p,uy)"} {"0"} {"0"} {"-d(-2*eta_ns*ux+p,vx)","-d(-eta_ns*(uy+vx),vx)","-d(-2*eta_ns*ux+p,vy)","-d(-eta_ns*(uy+vx),vy)"} {"-d(-eta_ns*(vx+uy),vx)","-d(-2*eta_ns*vy+p,vx)","-d(-eta_ns*(vx+uy),vy)","-d(-2*eta_ns*vy+p,vy)"} {"0"} {"0"} {"-d(-2*eta_ns*ux+p,px)","-d(-eta_ns*(uy+vx),px)","-d(-2*eta_ns*ux+p,py)","-d(-eta_ns*(uy+vx),py)"} {"-d(-eta_ns*(vx+uy),px)","-d(-2*eta_ns*vy+p,px)","-d(-eta_ns*(vx+uy),py)","-d(-2*eta_ns*vy+p,py)"} {"0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","-d(F_x_ns-rho_ns*(u*ux+v*uy),Az)","-d(F_y_ns-rho_ns*(u*vx+v*vy),Az)","-d(-divU_ns,Az)","0","-d(F_x_ns-rho_ns*(u*ux+v*uy),u)","-d(F_y_ns-rho_ns*(u*vx+v*vy),u)","-d(-divU_ns,u)","0","-d(F_x_ns-rho_ns*(u*ux+v*uy),v)","-d(F_y_ns-rho_ns*(u*vx+v*vy),v)","-d(-divU_ns,v)","0","-d(F_x_ns-rho_ns*(u*ux+v*uy),p)","-d(F_y_ns-rho_ns*(u*vx+v*vy),p)","-d(-divU_ns,p)"} {"0","0","0","0"} {"0","F_x_ns-rho_ns*(u*ux+v*uy)","F_y_ns-rho_ns*(u*vx+v*vy)","-divU_ns"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"-d(-2*eta_ns*ux+p,Az)","-d(-eta_ns*(uy+vx),Az)"} {"-d(-eta_ns*(vx+uy),Az)","-d(-2*eta_ns*vy+p,Az)"} {"0","0"} {"0","0"} {"-d(-2*eta_ns*ux+p,u)","-d(-eta_ns*(uy+vx),u)"} {"-d(-eta_ns*(vx+uy),u)","-d(-2*eta_ns*vy+p,u)"} {"0","0"} {"0","0"} {"-d(-2*eta_ns*ux+p,v)","-d(-eta_ns*(uy+vx),v)"} {"-d(-eta_ns*(vx+uy),v)","-d(-2*eta_ns*vy+p,v)"} {"0","0"} {"0","0"} {"-d(-2*eta_ns*ux+p,p)","-d(-eta_ns*(uy+vx),p)"} {"-d(-eta_ns*(vx+uy),p)","-d(-2*eta_ns*vy+p,p)"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"-d(F_x_ns-rho_ns*(u*ux+v*uy),Azx)","-d(F_x_ns-rho_ns*(u*ux+v*uy),Azy)"} {"-d(F_y_ns-rho_ns*(u*vx+v*vy),Azx)","-d(F_y_ns-rho_ns*(u*vx+v*vy),Azy)"} {"-d(-divU_ns,Azx)","-d(-divU_ns,Azy)"} {"0","0"} {"-d(F_x_ns-rho_ns*(u*ux+v*uy),ux)","-d(F_x_ns-rho_ns*(u*ux+v*uy),uy)"} {"-d(F_y_ns-rho_ns*(u*vx+v*vy),ux)","-d(F_y_ns-rho_ns*(u*vx+v*vy),uy)"} {"-d(-divU_ns,ux)","-d(-divU_ns,uy)"} {"0","0"} {"-d(F_x_ns-rho_ns*(u*ux+v*uy),vx)","-d(F_x_ns-rho_ns*(u*ux+v*uy),vy)"} {"-d(F_y_ns-rho_ns*(u*vx+v*vy),vx)","-d(F_y_ns-rho_ns*(u*vx+v*vy),vy)"} {"-d(-divU_ns,vx)","-d(-divU_ns,vy)"} {"0","0"} {"-d(F_x_ns-rho_ns*(u*ux+v*uy),px)","-d(F_x_ns-rho_ns*(u*ux+v*uy),py)"} {"-d(F_y_ns-rho_ns*(u*vx+v*vy),px)","-d(F_y_ns-rho_ns*(u*vx+v*vy),py)"} {"-d(-divU_ns,px)","-d(-divU_ns,py)"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"-2*eta_ns*ux+p","-eta_ns*(uy+vx)"} {"-eta_ns*(vx+uy)","-2*eta_ns*vy+p"} {"0","0"} 1 1 1 1 1 1 1 1 1 {"Az","u","v","p"} Azy -Azx 1 curlAx_qa curlAy_qa Bx_qa/(mur_qa*mu0_qa) By_qa/(mur_qa*mu0_qa) mu0_qa*mur_qa mu0_qa*murxx_qa mu0_qa*murxy_qa mu0_qa*muryx_qa mu0_qa*muryy_qa sigma_qa*deltaV_qa/L_qa Jpz_qa+Jvz_qa+Jez_qa Jz_qa*(vx_qa*By_qa-vy_qa*Bx_qa+deltaV_qa/L_qa) Wm_qa dVol_qa*W_qa 0.5*(Hx_qa*Bx_qa+Hy_qa*By_qa) -Jz_qa*By_qa Jz_qa*Bx_qa sqrt(abs(FLtzx_qa)^2+abs(FLtzy_qa)^2) sqrt(abs(Mx_qa)^2+abs(My_qa)^2) sqrt(abs(Brx_qa)^2+abs(Bry_qa)^2) sqrt(abs(Hx_qa)^2+abs(Hy_qa)^2) sqrt(abs(Bx_qa)^2+abs(By_qa)^2) abs(Jz_qa) sigma_qa*Evz_qa vx_qa*By_qa-vy_qa*Bx_qa abs(Evz_qa) sqrt(abs(vx_qa)^2+abs(vy_qa)^2) sqrt(u^2+v^2) vx-uy ux+vy rho_ns*U_ns*h/eta_ns rho_ns*(u*ux+v*uy)+px-F_x_ns-eta_ns*(2*uxx+uyy+vxy) rho_ns*(u*vx+v*vy)+py-F_y_ns-eta_ns*(vxx+uyx+2*vyy) rho_ns*u rho_ns*v eta_ns rho_ns nojac(1/max(2*rho_ns*sqrt(emetric(u,v)),48*eta_ns/h^2)) 0.5*nojac(if(u^2+v^2<sqrt(eps),h*U_ref_ns,(u^2+v^2)/sqrt(emetric(u,v)))) rho_ns*divU_ns 0 0 normB_qa/mu0_qa 1 0 0 0 1 Az murxx_qa Bx_qa/mu0_qa-Hx_qa 0 By_qa/mu0_qa-Hy_qa 0 1 0 0 1 1/mur_qa 0 0 1/mur_qa 0 0 rho eta mu0*Mv*d(Hx_qa,x) mu0*Mv*d(Hy_qa,y) 0.5 0.25 sc 0.35 1 0.1 0 Lagp2p1 Lagp2p1 -test(nojac(rho_ns)*(nojac(u)*ux+nojac(v)*uy)+px-nojac(eta_ns)*(2*uxx+uyy+vxy))*taum_ns*res_u_ns-test(nojac(rho_ns)*(nojac(u)*vx+nojac(v)*vy)+py-nojac(eta_ns)*(vxx+uyx+2*vyy))*taum_ns*res_v_ns-test(divU_ns)*tauc_ns*res_p_ns 0 (d(x,xi1)^2+d(x,xi2)^2)^2+2*(d(y,xi1)*d(x,xi1)+d(y,xi2)*d(x,xi2))^2+(d(y,xi1)^2+d(y,xi2)^2)^2 U_ns d(x,xi1)^2+d(x,xi2)^2 d(y,xi1)*d(x,xi1)+d(y,xi2)*d(x,xi2) d(y,xi1)^2+d(y,xi2)^2 -nojac(0.5*min(ck_ns*sqrt((tauc_ns*res_p_ns/(nojac(rhoint_g1_ns/vol_g1_ns)*nojac(sqrt(u2int_g1_ns/vol_g1_ns))))^2+(taum_ns*res_u_ns)^2+(taum_ns*res_v_ns)^2),U_ref_ns)*min(gijgij_ns^(-0.25),rho_ns*U_ref_ns/(48*eta_ns)))*rho_ns*(g11_ns*(ux*test(ux)+vx*test(vx))+g21_ns*(uy*test(ux)+vy*test(vx))+g21_ns*(ux*test(uy)+vx*test(vy))+g22_ns*(uy*test(uy)+vy*test(vy))) {0,0,0} {0,0,0} {1,2,1} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","-u-U0in_ns*nx_ns","-v-U0in_ns*ny_ns","0"} {"0","-u","-v","0"} {"0","-u","-v","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","test(-u-U0in_ns*nx_ns)","test(-v-U0in_ns*ny_ns)","0"} {"0","test(-u)","test(-v)","0"} {"0","test(-u)","test(-v)","0"} {"0","0","0","0"} {"-d(dVolbnd_qa*ny_qa*H0x_qa,Az)","0","0","0","-d(dVolbnd_qa*ny_qa*H0x_qa,u)","0","0","0","-d(dVolbnd_qa*ny_qa*H0x_qa,v)","0","0","0","-d(dVolbnd_qa*ny_qa*H0x_qa,p)","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"dVolbnd_qa*ny_qa*H0x_qa","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} 1 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 1 1 1 1 1 1 1 1 1 1tG( 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 {"","","",""} {"","","",""} {"","","",""} {"","","",""} {"","","",""} {"","","",""} {"","","",""} {"","","",""} {"","","",""} {"","","",""} {"Az","u","v","p"} 1 unx*(Hy_qa_down-Hy_qa_up)-uny*(Hx_qa_down-Hx_qa_up) -0.5*(Bx_qa_up*Hx_qa_up+By_qa_up*Hy_qa_up)*dnx+(dnx*Hx_qa_up+dny*Hy_qa_up)*Bx_qa_up -0.5*(Bx_qa_down*Hx_qa_down+By_qa_down*Hy_qa_down)*unx+(unx*Hx_qa_down+uny*Hy_qa_down)*Bx_qa_down -0.5*(Bx_qa_up*Hx_qa_up+By_qa_up*Hy_qa_up)*dny+(dnx*Hx_qa_up+dny*Hy_qa_up)*By_qa_up -0.5*(Bx_qa_down*Hx_qa_down+By_qa_down*Hy_qa_down)*uny+(unx*Hx_qa_down+uny*Hy_qa_down)*By_qa_down -Jsz_qa*By_qa Jsz_qa*Bx_qa sqrt(abs(FsLtzx_qa)^2+abs(FsLtzy_qa)^2) eta_ns*(2*nx_ns*ux+ny_ns*(uy+vx)) eta_ns*(2*nx_ns*ux+ny_ns*(uy+vx)) eta_ns*(2*nx_ns*ux+ny_ns*(uy+vx)) eta_ns*(2*nx_ns*ux+ny_ns*(uy+vx)) -nx_ns*p+2*nx_ns*eta_ns*ux+ny_ns*eta_ns*(uy+vx) -nx_ns*p+2*nx_ns*eta_ns*ux+ny_ns*eta_ns*(uy+vx) -nx_ns*p+2*nx_ns*eta_ns*ux+ny_ns*eta_ns*(uy+vx) -nx_ns*p+2*nx_ns*eta_ns*ux+ny_ns*eta_ns*(uy+vx) eta_ns*(nx_ns*(vx+uy)+2*ny_ns*vy) eta_ns*(nx_ns*(vx+uy)+2*ny_ns*vy) eta_ns*(nx_ns*(vx+uy)+2*ny_ns*vy) eta_ns*(nx_ns*(vx+uy)+2*ny_ns*vy) -ny_ns*p+nx_ns*eta_ns*(vx+uy)+2*ny_ns*eta_ns*vy -ny_ns*p+nx_ns*eta_ns*(vx+uy)+2*ny_ns*eta_ns*vy -ny_ns*p+nx_ns*eta_ns*(vx+uy)+2*ny_ns*eta_ns*vy -ny_ns*p+nx_ns*eta_ns*(vx+uy)+2*ny_ns*eta_ns*vy 0 0 nx ny flux*x/(L*mu0) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 u_in 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 dnx unx dnx unx dny uny dny uny 0 0 0 0 0 0 0 0 {0,0,0,0,0,0,0,0,0,0,0,0} {0,0,0,0,0,0,0,0,0,0,0,0} {1,1,1,2,3,4,5,1,4,3,4,3} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} {"0","0","0","0"} 1 1 2 3 4 1 1 1 1 1 1 1 1 1 {"","","",""} {"","","",""} {"","","",""} {"","","",""} {"Az","u","v","p"} 0 0 {0,0,0,0,0,0,0,0,0,0,0,0} {0,0,0,0,0,0,0,0,0,0,0,0} {1,1,2,2,2,2,2,2,2,2,1,1} 8.854187817000001e-012 4e-007*pi 10 elcplscalar {"1"} nojac(rho_ns) nojac(1) nojac(max((+(u)^2+(v)^2),(eta_ns/rho_ns/h)^2)) nojac(-1/max(emetric(u,v),(visc_vel_fact_ns*eta_ns/rho_ns)^2*emetric2)) ref ref ref ref ref ref ref ref 0 0 0 0 0 0 0 0 {"1","3"} {"2"} {"rhoint_g1_ns","vol_g1_ns","u2int_g1_ns","mdt2_cfl_g1_ns"} {"1","2","3","4"} {"4"} elconst nojac(sqrt(-mdt2_cfl_g1_ns))

4*pi*1e-7 [Wb/A/m] 0.001 [Pa*s] 5e-9 [m] 1/6/pi/eta/a 55*5.15*1000 [A/m] 4*pi*a^3/3 96500[C/mol] 1e16 [mol/m^3] 1.4e-3 [m] 1.3 [Wb/m^2] 0.05e-4[m] 0.005e-4[m] 1e-6 [m/s] 0 [m/s] 1.38e-23 [J/K] 298 [K] 1000 [kg/m^3] Mv maximum Satn M a radius {0} {0} qa weak SI uq~ t҄ off stationary stationary auto 1.0E-6 25 tol 100 1 off on off 1.0 1.0E-4 10.0 off on 0.0010 25 lumped automatic auto on 1 4 tol 10 1 off const 1.0 minimal 1.0 1.0E-2 10.0 0.0010 0.01 range(0,0.1,1) 0 1 0.1 11 step none tlist free bdf_ida 0.01 off 15 off on on on on on on off on on 0.0010 5 1 0.1 0.75 linear off off maybe bweuler 0 off 6 0 300 0.0 0 lambda 0 step none off 1 off 0.0 0.0 0.0 on auto auto auto eliminate auto 1000 on auto on off off on off currgeom l2 10000000 longest weak on 0 1 2 1 fltpft 2 1.7 0.5 0.5 on off off sensitivity adjoint on cholesky analytic 500 10 1.0e-6 1.0e-6 1.0e-6 1.0e-6 0 off v,u,p v,u,p,Az on init_storedsol_radio Automatic 0 u_storedsol_radio Automatic 0 off off off off umfpack linsolver 0.0 0.1 0.7 nd on off nd on 1.0E-8 on off tol 2 1.0E-6 400.0 10000 left right 1 50 1 1.0 3 6 v 5000 512.0 off 2.0 on droptol gmres 0.02 100 0.8 on on shape regular on 2 2 off Geom1 on on Az 1e-3 1 umfpack linsolver 0.0 0.1 0.7 nd on off nd on 1.0E-8 on off tol 2 1.0E-6 400.0 10000 left right 1 50 1 1.0 3 6 v 5000 512.0 off 2.0 on droptol gmres 0.02 100 0.8 on on shape regular on 2 2 off Geom1 on on u v p 1e-3 1 umfpack linsolver 0.0 0.1 0.7 nd on off nd on 1.0E-8 on off tol 2 1.0E-6 400.0 10000 left right 1 50 1 1.0 3 6 v 5000 512.0 off 2.0 on droptol gmres 0.02 100 0.8 on on shape regular on 2 2 off Geom1 on on 1 iter 0.5 1 1 20 10 1.0E-2 1 const off 1.0 1.0E-4 1.0E-2 10.0 minimal onevery 2 iter 0.5 1 1 20 10 1.0E-2 1 const off 1.0 1.0E-4 1.0E-2 10.0 minimal onevery off off off Geom1 0 off off off 1024836 COMSOL 3.5.0.603 1272658790281 1272656455500 off html off a4 off full off Geom1 boundary 1 -8.714906910878825E-4 0.001603383956653322 -5.483980203987171E-4 0.0016157423660149806 -1.0 1.0 1.9999999999999998E-4 1.9999999999999998E-4 0.01 -0.001143583227445998 0.001143583227445998 -0.0010820701932068488 0.0010820701932068488 3.659466327827197E-4 5.336721728081317E-4 0.011435832274459979 3.659466327827197E-4 5.336721728081317E-4 0.0 0.0 1.0 0.0 point headlight on 255 255 255 3.6594665E-4 5.3367217E-4 0.011435832 directional light 1 on 255 255 255 1.0 -1.0 1.0 directional light 2 on 255 255 255 -1.0 1.0 -1.0 directional light 3 on 255 255 255 -1.0 -1.0 1.0 directional light 4 on 255 255 255 1.0 -1.0 -1.0 on on on on off on on on on on on on off off off off 1.0 1.0 1.0 size cycle off off 0.5 orbit none none off off off off on off off on on on on on on 1.0E-6 intersection 1.0 normal off 2 1.0 off on off on off off on on 5 on 1 0.3 1.3 0.001 1 10 1.0 1.0 on 0 regular {"","","","","","","","","","","",""} {"","","","","","","","","","","",""} {"","","","","","","","","","","",""} {"","","","","","","","","","","",""} {"","","","","","","","","","","",""} {"","","","","","","","","","","",""} {"","",""} {"triaf","triaf","triaf"} {"","",""} on {"normB_qa"} on 0.009481810129708574 0.9219382169544671 on off T {"normB_qa"} off T Rainbow off on on 255,0,0 interp fill off {"normB_qa"} on off T {"normB_qa"} off T {"normB_qa"} on off T Rainbow off on on 255,0,0 20 off off step none off off {"Az"} on on off Wb/m {"Az"} off Wb/m Rainbow off on on 255,0,0 interp off sub {"Hx_qa","Hy_qa"} off A/m {"",""} off {"normB_qa"} off T 15 off 15 off step none step none arrow proportional 255,0,0 on 1 on {"u","v"} m/s off 255,0,0 {"normB_qa"} T Rainbow off on {"normB_qa"} off T 20 sub off step none step none 0.001 0.01 0.01 Inf 5000 on off 0.05 20 off 1 0.5 1.3 0.5 none off mass lines emforce_qa,khanforce_ns charge,partq,-1.602e-19 radius,partr,1e-4 9.1095e-31 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off Wb 0 0 stored step none off auto 4 on {"normB_qa"} off Wb 0 0 stored step none {"normB_qa"} on on off T Rainbow off on on 255,0,0 interp fill off {"Az"} on off Wb/m arc off {"Az"} Wb/m solid cyclecolor none off off 255,0,0 Rainbow off on on 255,0,0 interp fill {"Az"} off Wb/m off {"Az"} Wb/m solid cyclecolor none off off 255,0,0 255,0,0 0 0 stored step none on on on {"lin","lin"} on on 1 0 off {"normB_qa"} off T arc off {"normB_qa"} T solid cyclecolor none off off 255,0,0 Rainbow off on on 255,0,0 interp fill 200 {"0","1","0","0"} 5 off off step none {"normB_qa"} off T off {"normB_qa"} Wb solid cyclecolor none off off 255,0,0 {"0","0"} step none step none 255,0,0 0 0 stored step none on on on {"lin","lin"} on 0 {"Az"} off Wb/m element 2 {"Az"} off off Wb/m element 2 {"normB_qa"} off off T 10 off 10 off step none step none element 2 0 0 stored step none on ptd off 2 coorddata off off on 0 0 stored step none step none {"normB_qa"} off T {"0","0"} {} {} off solid cyclecolor none off 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