TALK=T;RUN(1,1) DISPLAY Numerical Schemes validation example: 2-d x-y, Cartesian, steady, elliptic simulation The problem considered is pure convection of scalar step in a prescribed recirculating velocity field. The flow geometry is a rectangular domain of 2 units length (X) and unit height (Y). The flow enters through the inlet in the range X=(-1,0), and then circulates clockwise through 180 degrees to exit in the range X=(0,1). At inlet, the scalar C=0 for X in the range (-1,-0.5) and C=1 in the range (0,1). Since physical diffusion is absent, this step change should be convected by the recirculating flow so as to appear as a step change at the outlet; thus, the exact solution is C=1 for X in the range (0,0.5) and C=0 for X in the range (0.5,1). The example compares the solution for 6 different linear schemes and 9 non-linear schemes for the discretisation of convection. NB: SATELLITE takes some time to process PIL commands ENDDIS PHOTON USE p 0.20443E+04 0.15633E+04 CR vec z 1 sh;gr ou z 1 stream 2d z 1 0 1 10 redr msg streamlines and vectors msg pressto continue pause cl;con usol z 1 fi;.1;gr z 1 msg upwind differencing scheme msg press to continue pause cl;con qsol z 1 fi;.1;gr z 1 msg QUICK scheme msg press to continue pause cl;con bsol z 1 fi;.1;gr z 1 msg SUPERBEE scheme msg press to end pause END USE GROUP 3. X-direction grid specification GROUP 4. Y-direction grid specification GROUP 7. Variables stored, solved & named ** linear schemes assigned to scalars ** USOL = uds CSOL = cds QSOL = quick LSOL = linear upwind 3SOL = cubic upwind FSOL = fromm's scheme ** non-linear schemes assigned to scalars ** SSOL = SMART KSOL = KOREN MSOL = MINMOD VSOL = VAN ALDBDA BSOL = SUPERBEE HSOL = HQUICK NSOL = VAN LEER 1 (NOLL) ZSOL = VAN LEER 2 (ZHU) OSOL = OSPRE GROUP 8. Terms (in differential equations) & devices ** Select numerical schemes for convection GROUP 11. Initialization of variable or porosity fields GROUP 13. Boundary conditions and special sources Patches for flow entry GROUP 15. Termination of sweeps GROUP 16. TERMINATION OF ITERATIONS GROUP 17. Under-relaxation devices GROUP 19. Data communicated by satellite to GROUND GROUP 20. Preliminary print-out GROUP 21. Print-out of variables OUTPUT(U1,N,N,N,N,N,N);OUTPUT(V1,N,N,N,N,N,N) GROUP 22. Spot-value print-out GROUP 23. Field print-out and plot control GROUP 24. Dumps for restarts