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Improvement on�M-AUSMPW+ scheme for all speed flow

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Taeyoon Kung

2022.10.12.

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Table of Contents

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Introduction

1.

Modification for all-speed

2.

Numerical result

3.

Conclusion

4.

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Table of Contents

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Introduction

1.

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Introduction

  • Characteristics which flow solver needs to have

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Robustness & Accuracy

Multi-physics

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Turbulent flow

Plasma

Ablation

All-speed flow

Moving object analysis

Efficiency

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Mesh optimization

Fast convergence

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Introduction

  • All-speed flow
    • The mathematical properties of the equations vary depending on the flow velocity range.
    • It is common for users to use single method for the whole flow field.
    • Most flux schemes which successfully solve the accuracy problem at supersonic speed have difficulties in obtaining low Mach number flow solution.

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Table of Contents

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Modification for all-speed

    • Governing equation
    • Baseline scheme
    • Asymptotic analysis
      • For governing equation
      • For discretized equation
    • Improvement on M-AUSMPW+

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Governing equations

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Baseline scheme: AUSMPW+/M-AUSMPW+

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Baseline scheme: AUSMPW+/M-AUSMPW+

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Asymptotic analysis for governing equations

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Behavior of M-AUSMPW+ on low speed

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Concave/convex

Inflection point

Local extrema

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Behavior of M-AUSMPW+ on low speed

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Behavior of M-AUSMPW+ on low speed

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Behavior of M-AUSMPW+ on low speed

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Behavior of M-AUSMPW+ on low speed

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(i, j)

(i+1, j)

(i-1, j)

(i, j-1)

(i, j+1)

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Behavior of M-AUSMPW+ on low speed

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Behavior of M-AUSMPW+ on low speed

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Behavior of M-AUSMPW+ on low speed

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Behavior of M-AUSMPW+ on low speed

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Behavior of M-AUSMPW+ on low speed

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Improvement on M-AUSMPW+

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Improvement on M-AUSMPW+

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Table of Contents

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Numerical result

3.

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Riemann problem 1

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Riemann problem 2

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Riemann problem 2

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Riemann problem 3

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Riemann problem 3

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Riemann problem 4

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Riemann problem 4

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Vortex flow

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Vortex flow

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Vortex flow

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Vortex flow

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Conclusion

4.

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Conclusion

  • Summary
    • LM-AUSMPW+ : extension of M-AUSMPW+ scheme for all-speed flow
      • Asymptotic analysis for the governing equations
      • Apply discretization to the equations by assuming 2D cartesian grid and first order FVM context
      • Asymptotic analysis to the discretized equations focusing on the difference between AUSMPW+ and M-AUSMPW+
      • Numerical dissipation of M-AUSMPW+ is controlled so that asymptotic behavior can be satisfied.

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  • Future work
    • More numerical tests needed
      • Ex) 2D bump…
    • Unresolved problem: “overheating problem”
      • Entropy problem in energy equation

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Thank you for listening

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Receding shock

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Receding shock

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Riemann problem 5

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Riemann problem 5

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Riemann problem 6

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2D bump

  • Result

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