Fluid Mechanics 6th Edition

ISBN 13
978-0124059351
ISBN 10
012405935X
Authors
David R Dowling Ph.D., Ira M. Cohen, Pijush K. Kundu
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978-0124059351 Chapter 6 Part 2
18 ut(i,j)=u(i,j)+dt*(-0.25*(... ( (u(i+1,j)+u(i,j))^2-(u(i,j)+u(i-1,j))^2 )/dx+... ( (u(i,j+1)+u(i,j))*(v(i+1,j)+v(i,j))-... (u(i,j)+u(i,j-1))*(v(i+1,j-1)+v(i,j-1)) )/dy )+... Visc*((u(i+1,j)+u(i-1,j)-2*u(i,j))/dx^2+... (u(i,j+1)+u(i,j-1)-2*u(i,j))/dy^2));end,endfor i=2:Nx+1,for j=2:Ny % temporary v-velocityvt(i,j)=v(i,j)+dt*(-0.25*(...( (u(i,j+1)+u(i,j))*(v(i+1,j)+v(i,j))-...(u(i-1,j+1)+u(i-1,j))*(v(i,j)+v(i-1,j)) )/dx+...( (v(i,j+1)+v(i,j))^2-(v(i,j)+v(i,j-1))^2 )/dy )+...Visc*((v(i+1,j)+v(i-1,j)-2*v(i,j))/dx^2+...(v(i,j+1)+v(i,j-1)-2*v(i,j))/dy^2));end,endfor it=1:MaxIt % solve for pressurefor i=2:Nx+1,for j=2:Ny+1p(i,j)=Beta*c(i,j)*...( (p(i+1,j)+p(i-1,j))/dx^2+...(p(i,j+1)+p(i,j-1))/dy^2 -...(rho/dt)*( (ut(i,j)-ut(i-1,j))/dx+...(vt(i,j)-vt(i,j-1))/dy ) )+...(1-Beta)*p(i,j);end,endend% correct the velocityu(2:Nx,2:Ny+1)=...ut(2:Nx,2:Ny+1)-...(dt/dx)*(p(3:Nx+1,2:Ny+1)-p(2:Nx,2:Ny+1));v(2:Nx+1,2:Ny)=...vt(2:Nx+1,2:Ny)-...(dt/dy)*(p(2:Nx+1,3:Ny+1)-p(2:Nx+1,2:Ny));time=time+dt % plot the resultsuu(1:Nx+1,1:Ny+1)=0.5*(u(1:Nx+1,2:Ny+2)+u(1:Nx+1,1:Ny+1)); (u(i,j+1)+u(i,j-1)-2*u(i,j))/dy^2));end,endfor i=2:Nx+1,for j=2:Ny % temporary v-velocityvt(i,j)=v(i,j)+dt*(-0.25*(...( (u(i,j+1)+u(i,j))*(v(i+1,j)+v(i,j))-...(u(i-1,j+1)+u(i-1,j))*(v(i,j)+v(i-1,j)) )/dx+...( (v(i,j+1)+v(i,j))^2-(v(i,j)+v(i,j-1))^2 )/dy )+...Visc*((v(i+1,j)+v(i-1,j)-2*v(i,j))/dx^2+...(v(i,j+1)+v(i,j-1)-2*v(i,j))/dy^2));end,endfor it=1:MaxIt % solve for pressurefor
Fluid Mechanics 6th Edition

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