Volume 9, Issue 1
Positivity-Preserving Runge-Kutta Discontinuous Galerkin Method on Adaptive Cartesian Grid for Strong Moving Shock

Jianming Liu, Jianxian Qiu, Mikhail Goman, Xinkai Li & Meilin Liu

Numer. Math. Theor. Meth. Appl., 9 (2016), pp. 87-110.

Published online: 2016-09

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  • Abstract

In order to suppress the failure of preserving positivity of density or pressure, a positivity-preserving limiter technique coupled with $h$-adaptive Runge-Kutta discontinuous Galerkin (RKDG) method is developed in this paper. Such a method is implemented to simulate flows with the large Mach number, strong shock/obstacle interactions and shock diffractions. The Cartesian grid with ghost cell immersed boundary method for arbitrarily complex geometries is also presented. This approach directly uses the cell solution polynomial of DG finite element space as the interpolation formula. The method is validated by the well documented test examples involving unsteady compressible flows through complex bodies over a large Mach numbers. The numerical results demonstrate the robustness and the versatility of the proposed approach.

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@Article{NMTMA-9-87, author = {}, title = {Positivity-Preserving Runge-Kutta Discontinuous Galerkin Method on Adaptive Cartesian Grid for Strong Moving Shock}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2016}, volume = {9}, number = {1}, pages = {87--110}, abstract = {

In order to suppress the failure of preserving positivity of density or pressure, a positivity-preserving limiter technique coupled with $h$-adaptive Runge-Kutta discontinuous Galerkin (RKDG) method is developed in this paper. Such a method is implemented to simulate flows with the large Mach number, strong shock/obstacle interactions and shock diffractions. The Cartesian grid with ghost cell immersed boundary method for arbitrarily complex geometries is also presented. This approach directly uses the cell solution polynomial of DG finite element space as the interpolation formula. The method is validated by the well documented test examples involving unsteady compressible flows through complex bodies over a large Mach numbers. The numerical results demonstrate the robustness and the versatility of the proposed approach.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2015.m1416}, url = {http://global-sci.org/intro/article_detail/nmtma/12368.html} }
TY - JOUR T1 - Positivity-Preserving Runge-Kutta Discontinuous Galerkin Method on Adaptive Cartesian Grid for Strong Moving Shock JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 87 EP - 110 PY - 2016 DA - 2016/09 SN - 9 DO - http://doi.org/10.4208/nmtma.2015.m1416 UR - https://global-sci.org/intro/article_detail/nmtma/12368.html KW - AB -

In order to suppress the failure of preserving positivity of density or pressure, a positivity-preserving limiter technique coupled with $h$-adaptive Runge-Kutta discontinuous Galerkin (RKDG) method is developed in this paper. Such a method is implemented to simulate flows with the large Mach number, strong shock/obstacle interactions and shock diffractions. The Cartesian grid with ghost cell immersed boundary method for arbitrarily complex geometries is also presented. This approach directly uses the cell solution polynomial of DG finite element space as the interpolation formula. The method is validated by the well documented test examples involving unsteady compressible flows through complex bodies over a large Mach numbers. The numerical results demonstrate the robustness and the versatility of the proposed approach.

Jianming Liu, Jianxian Qiu, Mikhail Goman, Xinkai Li & Meilin Liu. (2020). Positivity-Preserving Runge-Kutta Discontinuous Galerkin Method on Adaptive Cartesian Grid for Strong Moving Shock. Numerical Mathematics: Theory, Methods and Applications. 9 (1). 87-110. doi:10.4208/nmtma.2015.m1416
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