Changes between Version 24 and Version 25 of u/ehansen/buildcode


Ignore:
Timestamp:
11/03/11 15:14:57 (13 years ago)
Author:
ehansen
Comment:

—

Legend:

Unmodified
Added
Removed
Modified

  • u/ehansen/buildcode

    v24 v25  
    118118[[BR]]
    119119== Program Outline ==
    120 These are the basic steps in my program SEEQUOD (Solver for Euler EQUations in One Dimension).  SEEQUOD currently uses either an exact Riemann solver or the HLLC solver.  A Roe solver is to be added in the near future.  Also, SEEQUOD currently uses a first order Godunov upwind scheme, but again will later be updated to use higher order update schemes.  These steps should be general enough to apply to many codes that are used to solve the Euler Equations.
     120These are the basic steps in my program SEEQUOD (Solver for Euler EQUations in One Dimension).  SEEQUOD currently uses either an exact Riemann solver, an HLLC solver, or a Roe solver.  SEEQUOD currently uses a first order Godunov upwind scheme, but will later be updated to use higher order update schemes.  These steps should be general enough to apply to many codes that are used to solve the Euler Equations.
    121121
    122122* Read all input data necessary for problem
    … …  
    126126   * Impose CFL condition to get appropriate time step
    127127   * Begin flux calculation procedure
    128       * Solve local Riemann problem (exact or HLLC)
     128      * Solve local Riemann problem (exact, HLLC, or Roe)
    129129      * Use solution from Riemann solver to compute fluxes
    130130      * Repeat flux calculation procedure until fluxes are computed for all cells
    … …  
    145145||= 5 =||= 0.8 =||= 0.012 =||= 1.0 =||= -19.59745 =||= 1000.0 =||= 1.0 =||= -19.59745 =||= 0.01 =||
    146146
    147 Density, velocity, pressure, and internal energy were plotted for every test.  The following images show the numerical results (points) alongside the exact solution (line).  The first five groups of plots all used the exact Riemann solver.  Test 1 was also run with the HLLC solver. The density plot was made to compare it to the results of the exact solver.  Notice that the HLLC solver actually does a better job of resolving the left rarefaction. 
     147Using the exact Riemann solver, density, velocity, pressure, and internal energy were plotted for every test.  These plots correspond to the first five groups of plots.
     148
     149Test 1 was also run with the HLLC solver. The density plot was made to compare it to the results of the exact solver.  Notice that the HLLC solver actually does a better job of resolving the left rarefaction.  The exact solution has a much more noticeable entropy "glitch".  This is what we call that gap inside the left rarefaction.
     150
     151Test 1 was also run with the Roe solver in two different ways.  First as a basic Roe solver, and second with an entropy fix.  This entropy fix is required for transonic rarefactions, which is the case for the left rarefaction in Test 1. You can see that without this entropy fix, the gap inside that left rarefaction is very large and completely inaccurate.
     152
     153For all the plots, the numerical results (points) are alongside the exact solution (line). 
    148154
    149155All plots appear to be the same as those presented by Toro.  Therefore, the codes SEEQUOD and SEEQUODexact must be correct.
    150156
    151157
    152 [[CollapsibleStart(Test 1)]]
     158[[CollapsibleStart(Test 1 (Exact))]]
    153159|| [[Image(test1_density.png, width=500)]] || [[Image(test1_velocity.png, width=500)]] ||
    154160|| [[Image(test1_pressure.png, width=500)]] || [[Image(test1_intenergy.png, width=500)]] ||
    155161[[CollapsibleEnd]]
    156 [[CollapsibleStart(Test 2)]]
     162[[CollapsibleStart(Test 2 (Exact))]]
    157163|| [[Image(test2_density.png, width=500)]] || [[Image(test2_velocity.png, width=500)]] ||
    158164|| [[Image(test2_pressure.png, width=500)]] || [[Image(test2_intenergy.png, width=500)]] ||
    159165[[CollapsibleEnd]]
    160 [[CollapsibleStart(Test 3)]]
     166[[CollapsibleStart(Test 3 (Exact))]]
    161167|| [[Image(test3_density.png, width=500)]] || [[Image(test3_velocity.png, width=500)]] ||
    162168|| [[Image(test3_pressure.png, width=500)]] || [[Image(test3_intenergy.png, width=500)]] ||
    163169[[CollapsibleEnd]]
    164 [[CollapsibleStart(Test 4)]]
     170[[CollapsibleStart(Test 4 (Exact))]]
    165171|| [[Image(test4_density.png, width=500)]] || [[Image(test4_velocity.png, width=500)]] ||
    166172|| [[Image(test4_pressure.png, width=500)]] || [[Image(test4_intenergy.png, width=500)]] ||
    167173[[CollapsibleEnd]]
    168 [[CollapsibleStart(Test 5)]]
     174[[CollapsibleStart(Test 5 (Exact))]]
    169175|| [[Image(test5_density.png, width=500)]] || [[Image(test5_velocity.png, width=500)]] ||
    170176|| [[Image(test5_pressure.png, width=500)]] || [[Image(test5_intenergy.png, width=500)]] ||
    … …  
    174180|| [[Image(hllc_test1_density.png, width=500)]] || [[Image(test1_density.png, width=500)]] ||
    175181[[CollpasibleEnd]]
     182[[CollapsibleStart(Test 1 (Roe without entropy fix vs. Roe with entropy fix)]]
     183||= Roe without entropy fix =||= Roe with entropy fix =||
     184|| [[Image(roe_nofix_test1_density.png, width=500)]] || [[Image(roe_withfix_test1_density.png, width=500)]] ||
     185[[CollapsibleEnd]]