Performance and Resolution: Comparison of CLAWPACK and WENO, 2D Navier-Stokes equations

DMR Simulations

The simulation of DMR (Double Mach Reflection) problem for the 2d dimensional Navier-stokes equations was computed for the 2nd order CLAWPACK, symmetric WENO, and WENO-TCD to compare the performance and resolution capability, clearness and complexity found in the shear layer (aka mixing layer, or in the simple 3 shock inviscid theory: the slipline). In these compuations, done in the spirit of DNS (direct numerical simulation), the full resolution of turbulent, viscous, conduction, and shock thickness scales is unknown. These scales are definitely unresolved in coarse mesh simulations, however, may be either fully or partially resolved in the fine mesh simulations. The purpose of this comparison is to analyze how using different methods impacts the clarity of the diffusive phenomenon in underresolved (as by the scales mentioned) simulations. For example, the effects of upwinded/symmetrical stencils, order/bandwidth optimization, and other dissipative changes for the Clawpack, Weno, and WENO-TCD solvers is investigated. The problem set-up for these compuations is available under PerfectGasRamp, SutherlandRamp, PerfectGasRampGFM, and SutherlandRampGFM in the weno and clawpack: applications/euler/2D directories.

General Conclusions

Clawpack and WENO-TCD

• Methods and Parameters used
• DMR Problem dependent discontinuity flagging for WENO-TCD

GFM Ramp problem

• For these simulations the ramp boundary condition was enforced by using the ghost fluid method (GFM). For a Perfect gas, the Navier Stokes equations were for simulated for the following cases.

Constant viscosity and conductivity simulations

• Organized Table of Graphic links

• Problem setup
• Performance Comparison
• Selected Results

Temperature dependent viscosity and conductivity simulations ]

• Slip and No Sliip BC Sutherland Organized Table of Graphic Links:

DMRGFMSuthGraphicsTable

• Problem setup
• Performance Comparison
• Sutherland Temperature dependent Model
• Temperature dependent viscosity and conductivity with slip and noslip boundary conditions: Comparison with the Sutherland model for perfect (constant specific heat) nitrogen with the GFM Ramp BC

Rotated Ramp problem

• For these simulations the problem was rotated such that the ramp boundary was horizontal. The boundary condition in the startup region was enforced by using the ghost fluid method. A time dependent BC was also specifed at top.

Constant viscosity and conductivity simulations

• Organized Table of Graphic links

• Problem setup
• Performance Comparison
• Selected Results

Temperature dependent viscosity and conductivity simulations

• Slip and No Sliip BC Sutherland Organized Table of Graphic Links:

DMRSuthGraphicsTable

• Temperature dependent viscosity and conductivity with slip and noslip boundary conditions: Comparison with the Sutherland model for perfect (constant specific heat) nitrogen
• Sutherland Temperature dependent Model
• Problem setup
• Performance Comparison
• Selected Results