Revisit of dilation-based shock capturing for discontinuous Galerkin methods

doi:10.1007/s10483-018-2302-7

Abstract

Abstract: The idea of using velocity dilation for shock capturing is revisited in this paper, combined with the discontinuous Galerkin method. The value of artificial viscosity is determined using direct dilation instead of its higher order derivatives to reduce cost and degree of difficulty in computing derivatives. Alternative methods for estimating the element size of large aspect ratio and smooth artificial viscosity are proposed to further improve robustness and accuracy of the model. Several benchmark tests are conducted, ranging from subsonic to hypersonic flows involving strong shocks. Instead of adjusting empirical parameters to achieve optimum results for each case, all tests use a constant parameter for the model with reasonable success, indicating excellent robustness of the method. The model is only limited to third-order accuracy for smooth flows. This limitation may be relaxed by using a switch or a wall function. Overall, the model is a good candidate for compressible flows with potentials of further improvement.

Key words: artificial viscosity, Navier-Stokes equations, nonlinear Galerkin methods, Fourier methods, discontinuous Galerkin method, compressible flow

2010 MSC Number:

76M10

Jian YU, Chao YAN, Zhenhua JIANG. Revisit of dilation-based shock capturing for discontinuous Galerkin methods. Applied Mathematics and Mechanics (English Edition), 2018, 39(3): 379-394.

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