Overleg:Shallow water equations

Ik probeer de vergelijkingen er ook nog even netje bij te maken, maar dat is nog best lastig. Willem 22 Dec 2008 17:10 (CET)

<math> \begin{align} \frac {\partial W_{X,Y}}{\partial t}\cdot DX \cdot DY_X=& u_{x,Y} \cdot W_{x,Y}*DY_{x}-u_{x+1,Y} \cdot W_{x+1,Y} \cdot DY_{x+1}+ \\

                                    & v_{X,y}*W_{X,y}*DX-v_{X,y+1}*W_{X,y+1}*DX

\end{align} </math>

<math> \frac {\partial u_{x,Y}}{\partial t}\cdot DX \cdot DY_x \cdot W_{xY} =impuls_{normaal}+impuls_{tangentieel}+zwaartekracht+kromming+coriolis+getijkracht+frictie </math>

<math> impuls_{normaal}=\frac {W_{x-1,Y} \cdot u_{x-1,y}^2 \cdot DY_{x-1} -W_{x+1,Y} \cdot u_{x+1,y}^2 \cdot DY_{x+1}} {2} </math>

<math> impuls_{tangentieel}=W_{x,y} \cdot v_{x,y}^2 \cdot DX -W_{x+1,y} \cdot u_{x+1,y}^2 \cdot DX </math>

<math> dwdt[x][y]=u[x][y]*uW[x][y]*dyo[x]-u[x+1][y]*uW[x+1][y]*dyo[x+1]+ (v[x][y]*vW[x][y]-v[x][y+1]*vW[x][y+1])*DX; W[x][y]+=dwdt[x][y]*DT/DX/dym[x];

dudt[x][y]=(uW[x-1][y]*u[x-1][y]*u[x-1][y]*dyo[x-1]-uW[x+1][y]*u[x+1][y]*u[x+1][y]*dyo[x+1])/2.0+ //impuls transport

                  .5*g*(H[x-1][y]-H[x][y])*dyo[x]*uW[x][y]+                                                //potentiele energie
                  ( LOW[x][y]*(v[x][y]+v[x-1][y])*(u[x][y]+u[x][y-1])-                                     
                      ROW[x][y]*(v[x][y+1]+v[x-1][y+1])*(u[x][y+1]+u[x][y]) )/4.0*DX+                      //tangentieel impuls transport
                      -u[x][y]/R*dyo[x]*DX*vopu[x][y]*sino[x]+                                             //curvature
                      -2*omega*vopu[x][y]*sino[x]*uW[x][y]*DX*dyo[x]+                                      //coriolis kracht
                      uGM[x][y]*uW[x][y]*DX*dyo[x]+                                                        //maan getij kracht
                      -u[x][y]*0.01*DX*dyo[x];                                            //frictie

       dvdt[x][y]=(vW[x][y-1]*v[x][y-1]*v[x][y-1]-vW[x][y+1]*v[x][y+1]*v[x][y+1])/2.0*DX+
                  .5*g*(H[x][y-1]-H[x][y])*vW[x][y]*DX+
                  ( LOW[x][y]*(u[x][y]+u[x][y-1])*(v[x][y]+v[x-1][y])*dyo[x]-
                      LBW[x][y]*(u[x+1][y]+u[x+1][y-1])*(v[x+1][y]+v[x][y])*dyo[x+1] )/4.0+   
                      uopv[x][y]/R*dym[x]*DX*uopv[x][y]*sinm[x]+
                      2*omega*uopv[x][y]*sinm[x]*vW[x][y]*DX*dym[x]+
                      vGM[x][y]*vW[x][y]*DX*dym[x]+
                      -v[x][y]*0.01*DX*dym[x];

       dudt[x][y]/=uW[x][y]*DX*dyo[x];
       dvdt[x][y]/=vW[x][y]*DX*dym[x];

</math>