An effective limiting algorithm for particle-based numerical simulations of compressible flows

Abstract

Eulerian computational fluid dynamics (CFD) and Lagrangian computational structural dynamics (CSD) are used extensively in the aerospace industry. Combined mesh-based Eulerian and particle-based Lagrangian algorithms arevery effective for modelling and simulation due to the increased efficiency of combining the two numerical simulations. However, when compressible flows are simulated using a particle-based algorithm, calculations of strong discontinuity, such as a shock wave, may become unstable. In the present study, a numerical limiter is integrated with a particle-based CFD code to remedy this instability. The limiting algorithm incorporates an ‘averaging’ technique which calculates average values using the properties of neighbouring particles (also known as material points), including mass, momentum and energy. These averaged values are then input to a min-mode limiter to eliminate numerical noise and incur dissipation in the flow in areas with steep property gradients. The results of this algorithm show very stable solutions with minimal oscillations when applied to the one-dimensional shock tube problem and an increased accuracy with reduced oscillations for a two-dimensional cylinder cross-flow problem.

Keywords:

• limiter
• material point
• simulation
• compressible
• shock tube
• particle-based solver

Acknowledgements

Financial support and the MPM code used for this research were provided by Advanced Dynamics Incorporated (ADI). ADI's MPM code is developed according to commercial CFD standards and has been used in other publications (seeHu et al. 2010a, 2010b) and ADI assisted with the editing of this paper for final submission. Additionally, the referees provided many suggestions for improvements that greatly enhanced this paper.