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Liska and Wendroff 2D Riemann Tests

Initial Values:

4 quadrants,each with independent values for density (d), Pressure (P), and velocity components (vex) and vi).

Ending Condition:

• Time, t = T given for each test, between 0.2 and 0.3 time units

Grid:

• Domain: 0.0 < x <1.0, 0.0 < y < 1.0 , divided into 4 quadrants:
  • Upper Left: 0.0 < x < 0.5, 0.5 < y < 1.0
  • Upper Right: 0.5 < x < 1.0, 0.5 < y < 1.0
  • Lower Left: 0.0 < x < 0.5, 0.0 < y < 0.5
  • Lower Right:0.5 < x < 1.0, 0.0 < y < 0.5
• 400 x 400 cells.
• All boundaries are free or natural boundaries.

Hydrodynamics Settings:

• Adiabatic index: Gamma = 1.4
• CFL number: 0.8, initial step 0.4 (standard)
• Flattening: minimum 0.0, maximum 1.0 (standard)

The code and configuration files plus output for Fyris to run the 2D Riemann problems are included in the code download.

Results: Initial and Final States:

Note: Here the use of the contouring rainbow colour palette helps to show small defects that are invisible with a more continuous table, such as used in the L&W reference. This colour table is available here in the resources section. Most of the extended linear features are remnants of the initial contact dicontinuities from the initial conditions. As Fyris preserves stationary contact discontinuties very well, the first changes in density as the reimann problem get started are preserved to late times, where a more diffusive method may not do so. These 'glitches' are small, < 1%, but show up in the contours.

Test 3	Test 4	Test 6
Test 12	Test 15	Test 17