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The Harten-Lax-van Leer Discontinuities (HLLD) Riemann solver enhances robustness for nonlinear elasticity problems. This advanced method, combined with piecewise parabolic methods and level set algorithms, effectively captures material interfaces and reduces oscillations.

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Area of Science:

  • Computational fluid dynamics
  • Solid mechanics
  • Numerical analysis

Background:

  • High-load conditions in nonlinear elasticity present challenges for numerical simulations.
  • Accurate resolution of complex wave structures and material interfaces is crucial.

Purpose of the Study:

  • To apply Harten-Lax-van Leer (HLL)-type solvers to Riemann problems in nonlinear elasticity under high-load conditions.
  • To evaluate the performance of the HLLD Riemann solver against HLL and HLLC solvers.
  • To develop a robust numerical scheme for multi-material interfaces.

Main Methods:

  • Application of Harten-Lax-van Leer (HLL)-type solvers, specifically HLLD, for nonlinear elasticity.
  • Extension of the Godunov finite volume scheme to higher order accuracy using the piecewise parabolic method (PPM).
  • Integration of a level set algorithm with the HLLD Riemann solver and a modified ghost method for multi-material interface tracking.

Main Results:

  • The HLLD Riemann solver demonstrated superior robustness and efficiency in resolving complex nonlinear wave structures, outperforming HLL and HLLC solvers.
  • The piecewise parabolic method (PPM) extended the Godunov scheme to higher accuracy.
  • The combined scheme effectively captured material interfaces in both 'stick' and 'slip' problems, significantly suppressing spurious oscillations.

Conclusions:

  • The HLLD Riemann solver is highly effective for nonlinear elasticity problems with complex wave phenomena.
  • The integration of HLLD, PPM, and level set algorithms provides a robust and accurate method for simulating multi-material interfaces.
  • This numerical scheme offers significant improvements in interface capturing and oscillation suppression.