# LaTeX2HTML 2002-2-1 (1.70)
# Associate images original text with physical files.
$key = q/displaystyleleft.DP{psi}{t}right|_{Dvect{i}}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyleleft.DP{psi}{t}right|_{i,j}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystylepsi_{i}^{n}+left.DP{psi}{t}right|^{n}Deltat+left.frac{1}{2}DP[2]{psi}{r}right|^{n}(Deltat)^{2}+O(Deltat^{3});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}psi_{i}^{n+1}=psi_{i}^{n}+left.DP{psi}{t}right|_{i}^{n}Deltat+frac{{psi}{t}right|_{i}^{n}(Deltat)^{2}+cdotcdotcdot.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/FH_{x},FH_{y};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/AtimesB;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/A,B;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyleu_{i+frac{1}{2},j}^{n}(psi_{i,j}^{n}+psi_{i+1,j}^{n})frac{Deltat}{Deltax},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystylefrac{1}{psi_{i,j+frac{1}{2}}^{*}}left[frac{1}{2}(|v_{i,j+frac{1}{2}}}}^{n})^{2})frac{psi_{i,j+1}^{*}-psi_{i,j}^{*}}{Deltay}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}DP[2]{psi}{t}=-DP{}{x}left[uleft(-DP{}{x}(upsi)right)right]=DP{}{x}x}(upsi)right]=DP{}{x}left[u^{2}DP{psi}{x}right]{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{eqnarraystar}DP[2]{psi}{t}&=&-DP{}{x}left[uleft(-DP{}{x}(upsi)-DP{}{y}(vpsi)rigt[vpsileft(DP{u}{y}+DP{v}{x}right)right]{eqnarraystar};MSF=1.6;LFS=12;TAGS=R;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}DP{psi}{t}+DP{}{x}(upsi)=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}psi_{i}^{*}=psi_{i}^{n}-{F(psi_{i}^{n},psi_{i+1}^{n},u_{i+frac{1}{2si_{i-1}^{n},psi_{i}^{n},u_{i-frac{1}{2}}^{n})}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/0leqxleq1,0leqyleq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/tilde{u}_{1+frac{1}{2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}DP{psi}{t}=-{F(psi_{i}^{n},psi_{i+1}^{n},u_{i+frac{1}{2}}^{n})-F(psi_{i-1}^{n},psi_{i}^{n},u_{i-frac{1}{2}}^{n})}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}DP{psi}{t}+DP{}{x}(upsi)+DP{}{y}(vpsi)=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}DP{psi}{t}=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystylefrac{1}{4}left(psi_{i+1,j+1}^{*}+psi_{i,j+1}^{*}+psi_{i+1,j}^{*}+psi_{i,j}^{*}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/u_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}F(psi_{i}^{n},psi_{i+1}^{n},u_{i+frac{1}{2}}^{n})=[(u_{i+frac{1}{2}frac{1}{2}}^{n}|)psi_{i+1}^{n}]frac{1}{2Deltax},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}tilde{u}rightarrow0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/textstyle=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyle+DP{}{x}left.left[frac{1}{2}(|u|Deltax-Deltatu^{2})DP{psi}{x}-frac{1}{2}DeltatuvDP{psi}{y}right]right|_{i,j}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{eqnarraystar}F_{x}(psi_{i,j}^{n},psi_{i+1,j}^{n},u_{i+frac{1}{2},j}^{n})&=&[(u_|)psi_{i,j+1}^{n}]frac{Deltat}{2Deltay},{eqnarraystar};MSF=1.6;LFS=12;TAGS=R;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyletilde{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystylepsi_{i,j}^{*}-{F_{x}(psi_{i,j}^{*},psi_{i+1,j}^{*},tilde{u}_{i+frac{{x}(psi_{i-1,j}^{*},psi_{i,j}^{*},tilde{u}_{i-frac{1}{2},j})};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystylefrac{1}{psi}left[frac{1}{2}(|u|Deltax-Deltatu^{2})DP{psi}{x}-frac{1}{psi}{y}right]-frac{1}{2}Deltatuleft(DP{u}{x}+DP{v}{y}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyle-left.DP{}{x}(upsi)right|_{i,j}^{n}+DP{}{x}left.left(frac{1}{2}|u|DeltaxDP{psi}{x}right)right|_{i,j}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/psi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}frac{psi_{i}^{n+1}-psi_{i}^{n}}{Deltat}=-left.DP{}{x}(upsi)right|_{taxDP{psi}{x}right)right|_{i}^{n}+O(Deltax^{2}).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}mbox{max}left[underbrace{frac{|u_{i+frac{1}{2}}|Deltat}{Deltax}}_{A_{i}^{*}+psi_{i+1}^{*}+epsilon)}}_{C}right]leq1,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}mbox{max}left(frac{|tilde{u}_{i+frac{1}{2}}|Deltat}{Deltax}right)leq1,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystylepsi_{i,j}^{n+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/|u|_{i+frac{1}{2}}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyle-{F_{y}(psi_{i,j}^{*},psi_{i,j+1}^{*},tilde{v}_{i,j+frac{1}{2}})-F_{y}(psi_{i,j-1}^{*},psi_{i,j}^{*},tilde{v}_{i,j-frac{1}{2}})}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystylefrac{1}{psi}left[frac{1}{2}(|v|Deltay-Deltatv^{2})DP{psi}{y}-frac{1}{psi}{x}right]-frac{1}{2}Deltatvleft(DP{u}{x}+DP{v}{y}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{figure}center{{Depsf[][80mm]{ps-figslashinit.ps}{{{center{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}tilde{u}_{i+frac{1}{2}}=frac{(|u_{i+frac{1}{2}}^{n}|Deltax-Deltatu_*})}{(psi_{i}^{*}+psi_{i+1}^{*}+epsilon)Deltax}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystylefrac{1}{4}left(u_{i+frac{1}{2},j+1}^{n}+u_{i-frac{1}{2},j+1}^{n}+u_{i+frac{1}{2},j}^{n}+u_{i-frac{1}{2},j}^{n}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}DP{}{x}left(K_{impl}DP{psi}{x}right),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyletilde{v}_{i,j+frac{1}{2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystylefrac{1}{psi}left[frac{1}{2}(|u|Deltax-Deltatu^{2})DP{psi}{x}-frac{1}{2}DeltatuvDP{psi}{y}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/(;);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}DP[2]{psi}{t}=-DP{}{t}left[left(DP{}{x}(upsi)right)right]=-DP{}{x}lP{u}{t}right]+DP{}{x}left[u^{2}DP{psi}{x}right],{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/psi_{i}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/tilde{u},tilde{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/t+Deltatslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/Dvect{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{eqnarraystar}&&-frac{1}{2Deltax}left[left(-|u_{i}|left.DP{psi}{x}right|_{i}^{n}i}{x}right)right|_{i}^{n}+O(Deltax^{2}).{eqnarraystar};MSF=1.6;LFS=12;TAGS=R;AAT/;
$cached_env_img{$key} = q||;
$key = q/{eqnarraystar}&&-frac{1}{Deltax}left[left(u_{i}^{n}psi_{i}^{n}+frac{u_{i}^{n}}{2{}{x}(upsi)right|_{i}^{n}+O(Deltax^{2}),{eqnarraystar};MSF=1.6;LFS=12;TAGS=R;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyle-{[CF_{y}cdotFH_{y}+(1-CF_{y})cdotFL_{y}]_{i,j+frac{1}{2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}DP{psi}{t}+DP{}{x}(upsi)=DP{}{x}left(K_{impl}DP{psi}{x}right),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyleDP{psi}{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/(x_{m},y_{m})=(0.75,0.5);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystylefrac{1}{psi_{i+frac{1}{2},j}^{*}}left[frac{1}{2}(|u_{i+frac{1}{2},j}j}^{n})^{2})frac{psi_{i+1,j}^{*}-psi_{i,j}^{*}}{Deltax}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/Deltat,Deltaxrightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyle-left.DP{}{x}(upsi)right|_{i,j}^{n}-left.DP{}{y}(vpsi)right|_{i,j}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyleF_{y}(psi_{i.j}^{n},psi_{i,j+1}^{n},v_{i,j+frac{1}{2}}^{n});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}DP{psi}{t}=-left.DP{}{x}(upsi)right|_{i}^{n}+DP{}{x}left.left(frac{taxDP{psi}{x}right)right|_{i}^{n}+O(Deltax^{2}).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/C;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyleu_{i,j+frac{1}{2}}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyle-left.frac{1}{2}Deltatu_{i+frac{1}{2},j}^{n}v_{i+frac{1}{2},j}^{n}fr}{2}}^{*}-psi_{i+frac{1}{2},j-frac{1}{2}}^{*}}{Deltay}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/|u|_{i}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyletilde{u};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}-DP{}{x}(u_{d}psi),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyle-frac{1}{Deltax}left(u_{i+frac{1}{2}}^{n}frac{psi_{i}^{n}+psi_{i+1}^-u_{i-frac{1}{2}}^{n}frac{psi_{i}^{n}+psi_{i-1}^{n}}{2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}psi_{i}^{n+1}=psi_{i}^{*}-{F(psi_{i}^{*},psi_{i+1}^{*},tilde{u}_{i+{i-1}^{*},psi_{i}^{*},tilde{u}_{i-frac{1}{2}})}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}frac{psi^{n+1}-psi^{n}}{Deltat}=-DP{}{x}(u^{n+frac{1}{2}}psi^{n}),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/u_{i+frac{1}{2}}^{n},u_{i-frac{1}{2}}^{n},psi_{i+1}^{n},psi_{i-1}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{eqnarraystar}DP[2]{psi}{t}&=&-DP{}{x}left[uleft(-DP{}{x}(upsi)-DP{}{y}(vpsi)rig}left[v^{2}DP{psi}{y}+uvDP{psi}{x}right]{eqnarraystar};MSF=1.6;LFS=12;TAGS=R;AAT/;
$cached_env_img{$key} = q||;
$key = q/sim;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/omega=0.1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}mbox{max}left(frac{|u_{i+frac{1}{2}}|Deltat}{Deltax}right)leq1,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/(x_{0},y_{0})=(0.5,0.5);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/u_{i}^{n},psi_{i}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/I;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyle+DP{}{y}left.left[frac{1}{2}(|v|Deltay-Deltatv^{2})DP{psi}{y}-frac{1}{2}DeltatuvDP{psi}{x}right]right|_{i,j}^{n},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystylepsi_{i+frac{1}{2},j}^{*};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystylepsi_{i,j}^{n}-{F_{x}(psi_{i,j}^{n},psi_{i+1,j}^{n},u_{i+frac{1}{2},j-F_{x}(psi_{i-1,j}^{n},psi_{i,j}^{n},u_{i-frac{1}{2},j}^{n})};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyle-[CF_{x}cdotFH_{x}+(1-CF_{x})cdotFL_{x}]_{i-frac{1}{2},j}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyle-DP{}{x}(u^{n}psi^{n})-frac{1}{2}DeltatDP{}{x}left(psileft.DP{u}{t}right)right|^{n}+O(Deltat^{2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/Dvect{i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyle+sum_{I=1}^{N}DP{}{x^{I}}left.left[frac{1}{2}(|u^{I}|Deltax^{I}-Delt}{2}Deltatu^{I}u^{J}DP{psi}{x^{J}}right]right|_{Dvect{i}}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyle-DP{}{x}(u^{n+frac{1}{2}}psi^{n});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyle-sum_{I=1}^{N}DP{}{x^{I}}left.left[left(frac{1}{2}Deltatu^{I}sum_{J=1}^{N}DP{u^{J}}{x^{J}}right)psiright]right|_{Dvect{i}}^{n},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/u^{n+frac{1}{2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyle-frac{1}{2}left.DP{}{x}left[Deltatupsileft(DP{u}{x}+DP{v}{y}right)riDeltatvpsileft(DP{u}{x}+DP{v}{y}right)right]right|^{n}_{i,j}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/u;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyle+sum_{I=1}^{N}DP{}{x^{I}}left.left[frac{1}{2}(|u^{I}|Deltax^{I}-Deltac{1}{2}Deltatu^{I}u^{J}DP{psi}{y}right]right|_{Dvect{i}}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyle+DP{}{y}left.left[frac{1}{2}(|v|Deltay-Deltatv^{2})DP{psi}{y}-frac{1}{2}DeltatuvDP{psi}{x}right]right|_{i,j}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{figure}center{{Depsf[][80mm]{ps-figslashcenter2-1.ps}{{{{Depsf[][80mm]{ps-figslashcenter2-2.ps}{{{center{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyle-sum_{I=1}^{N}left.DP{}{x^{I}}(u^{I}psi)right|_{Dvect{i}}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/CF_{x}=CF_{y}=0.8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystylepsi_{i,j}^{*};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystylepsi_{i}^{n+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/Deltat=0.1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}tilde{u}=-u_{d},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{figure}center{{Depsf[][80mm]{ps-figslashupstream1.ps}{{{{Depsf[][80mm]{ps-figslashupstream2.ps}{{{center{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}left.DP{psi}{t}right|_{i}^{n}=-left.DP{}{x}(upsi)right|_{i}^{n}+DP{x}right]right|_{i}^{n}+O(Deltax^{2},Deltat^{2}).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}u_{d}=left{array{{ccl}-frac{K_{impl}}{psi}DP{psi}{x},&mbox{if}&psi>00,&mbox{if}&psi=0.array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyle-left.frac{1}{2}Deltatu_{i,j+frac{1}{2}}^{n}v_{i,j+frac{1}{2}}^{n}fr}{2}}^{*}-psi_{i-frac{1}{2},j+frac{1}{2}}^{*}}{Deltax}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/epsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/FL_{x},FL_{y};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/x^{I},u^{I};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyle-frac{1}{2Deltax}left[|u_{i+frac{1}{2}}^{n}|(psi_{i}^{n}-psi_{i+1}^{n})-|u_{i-frac{1}{2}}^{n}|(psi_{i-1}^{n}-psi_{i}^{n})right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}u^{n+frac{1}{2}}=frac{u^{n}+u^{n+1}}{2}+O(Deltat^{2}){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}u_{d,Dvect{i}}^{I}=left.0.5[|u^{I}Deltax^{I}-Deltat(u^{I})^{2}]frac^{J}frac{1}{psi}DP{psi}{x^{J}}right|_{Dvect{i}},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystylev_{i,j+frac{1}{2}}^{n}(psi_{i,j}^{n}+psi_{i,j+1}^{n})frac{Deltat}{Deltay},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/(uDeltatslashDeltax);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystylefrac{1}{8}left(psi_{i+1,j+1}^{*}+psi_{i,j+1}^{*}+2psi_{i+1,j}^{*}+2psi_{i,j}^{*}+psi_{i+1,j-1}^{*}+psi_{i,j-1}^{*}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/psi_{i}^{n+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/x=iDeltax,t=nDeltat;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/textstyleequiv;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyle-{F_{y}(psi_{i,j}^{n},psi_{i,j+1}^{n},v_{i,j+frac{1}{2}}^{n})-F_{y}(psi_{i,j-1}^{n},psi_{i,j}^{n},v_{i,j-frac{1}{2}}^{n})}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/psi^{n+1},u^{n+frac{1}{2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/CF_{x},CF_{y};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}u_{d,Dvect{i}}^{I}=left.0.5[|u^{I}Deltax^{I}-Deltat(u^{I})^{2}]fracI}sum_{J=1}^{N}DP{u^{J}}{x^{J}}right|_{Dvect{i}}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyletilde{u}_{i+frac{1}{2},j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/Deltat;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/10^{-15};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/tilde{u},tilde{u};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{eqnarraystar}u_{i+frac{1}{2}}^{n}&=&u_{i}^{n}+left.DP{u}{x}right|_{i}^{n}frac{Dright|_{i}^{n}(Deltax)^{2}+cdotcdotcdot.{eqnarraystar};MSF=1.6;LFS=12;TAGS=R;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystylepsi_{i}^{n}+left.DP{psi}{t}right|^{n}Deltat-frac{1}{2}(Deltat)^{2}DP{}{x}left(psileft.DP{u}{t}right)right|^{n}+O(Deltat^{3}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyle-left.DP{}{y}(vpsi)right|_{i,j}^{n}+DP{}{y}left.left(frac{1}{2}|v|De{i,j}^{n}-frac{1}{2}left.DP[2]{psi}{t}right|_{i,j}^{n}Deltat.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}DP{psi}{t}+Ddiv(Dvect{v}psi)=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{figure}center{{Depsf[][80mm]{ps-figslashfct3.ps}{{{{Depsf[][80mm]{ps-figslashfct4.ps}{{{center{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystylepsi_{i+frac{1}{2},j+frac{1}{2}}^{*};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyle-[CF_{y}cdotFH_{y}+(1-CF_{y})cdotFL_{y}]_{i,j-frac{1}{2}}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystyleF_{x}(psi_{i,j}^{n},psi_{i+1,j}^{n},u_{i+frac{1}{2},j}^{n});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/(K_{impl}=0.5[|u|Deltax-Deltatu^{2}]);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/[;];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystylefrac{1}{psi}left[frac{1}{2}(|v|Deltay-Deltatv^{2})DP{psi}{y}-frac{1}{2}DeltatuvDP{psi}{x}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{figure}center{{Depsf[][80mm]{ps-figslashfct1.ps}{{{{Depsf[][80mm]{ps-figslashfct2.ps}{{{center{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q||;
$key = q/Deltat=0.05;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/F_{x},F_{y};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/Deltax=Deltay=0.01;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{figure}center{{Depsf[][80mm]{ps-figslashmpdata1.ps}{{{{Depsf[][80mm]{ps-figslashmpdata2.ps}{{{center{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q||;
$key = q/tilde{u};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/(u,v)=(-omega(y-y_{0}),omega(x-x_{0}));MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}left.DP{psi}{t}right|^{n}=-DP{}{x}(u^{n}psi^{n})+left.DP{}{x}left(f{2}DP{psi^{n}}{x}right)right|^{n}+O(Deltat^{2}),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/displaystylepsi_{i,j}^{n}-{[CF_{x}cdotFH_{x}+(1-CF_{x})cdotFL_{x}]_{i+frac{1}{2},j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/|u_{i+frac{1}{2}}^{n}|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
$key = q/{displaymath}DP{psi}{t}=-DP{}{x}(upsi)+DP{}{x}left(KDP{psi}{x}right),;K=frac{1}{2}|u|Deltax,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q||;
1;