Volume 17, Issue 2
High Order Finite Difference Methods with Subcell Resolution for Stiff Multispecies Discontinuity Capturing

Wei Wang, Chi-Wang Shu, H. C. Yee, Dmitry V. Kotov & Björn Sjögreen

Commun. Comput. Phys., 17 (2015), pp. 317-336.

Published online: 2018-04

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  • Abstract

In this paper, we extend the high order finite-difference method with subcell resolution (SR) in [34] for two-species stiff one-reaction models to multispecies and multireaction inviscid chemical reactive flows, which are significantly more difficult because of the multiple scales generated by different reactions. For reaction problems, when the reaction time scale is very small, the reaction zone scale is also small and the governing equations become very stiff. Wrong propagation speed of discontinuity may occur due to the underresolved numerical solution in both space and time. The present SR method for reactive Euler system is a fractional step method. In the convection step, any high order shock-capturing method can be used. In the reaction step, an ODE solver is applied but with certain computed flow variables in the shock region modified by the Harten subcell resolution idea. Several numerical examples of multispecies and multireaction reactive flows are performed in both one and two dimensions. Studies demonstrate that the SR method can capture the correct propagation speed of discontinuities in very coarse meshes.

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@Article{CiCP-17-317, author = {Wei Wang , and Chi-Wang Shu , and H. C. Yee , and Dmitry V. Kotov , and Björn Sjögreen , }, title = {High Order Finite Difference Methods with Subcell Resolution for Stiff Multispecies Discontinuity Capturing}, journal = {Communications in Computational Physics}, year = {2018}, volume = {17}, number = {2}, pages = {317--336}, abstract = {

In this paper, we extend the high order finite-difference method with subcell resolution (SR) in [34] for two-species stiff one-reaction models to multispecies and multireaction inviscid chemical reactive flows, which are significantly more difficult because of the multiple scales generated by different reactions. For reaction problems, when the reaction time scale is very small, the reaction zone scale is also small and the governing equations become very stiff. Wrong propagation speed of discontinuity may occur due to the underresolved numerical solution in both space and time. The present SR method for reactive Euler system is a fractional step method. In the convection step, any high order shock-capturing method can be used. In the reaction step, an ODE solver is applied but with certain computed flow variables in the shock region modified by the Harten subcell resolution idea. Several numerical examples of multispecies and multireaction reactive flows are performed in both one and two dimensions. Studies demonstrate that the SR method can capture the correct propagation speed of discontinuities in very coarse meshes.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.250214.130814a}, url = {http://global-sci.org/intro/article_detail/cicp/10960.html} }
TY - JOUR T1 - High Order Finite Difference Methods with Subcell Resolution for Stiff Multispecies Discontinuity Capturing AU - Wei Wang , AU - Chi-Wang Shu , AU - H. C. Yee , AU - Dmitry V. Kotov , AU - Björn Sjögreen , JO - Communications in Computational Physics VL - 2 SP - 317 EP - 336 PY - 2018 DA - 2018/04 SN - 17 DO - http://doi.org/10.4208/cicp.250214.130814a UR - https://global-sci.org/intro/article_detail/cicp/10960.html KW - AB -

In this paper, we extend the high order finite-difference method with subcell resolution (SR) in [34] for two-species stiff one-reaction models to multispecies and multireaction inviscid chemical reactive flows, which are significantly more difficult because of the multiple scales generated by different reactions. For reaction problems, when the reaction time scale is very small, the reaction zone scale is also small and the governing equations become very stiff. Wrong propagation speed of discontinuity may occur due to the underresolved numerical solution in both space and time. The present SR method for reactive Euler system is a fractional step method. In the convection step, any high order shock-capturing method can be used. In the reaction step, an ODE solver is applied but with certain computed flow variables in the shock region modified by the Harten subcell resolution idea. Several numerical examples of multispecies and multireaction reactive flows are performed in both one and two dimensions. Studies demonstrate that the SR method can capture the correct propagation speed of discontinuities in very coarse meshes.

Wei Wang, Chi-Wang Shu, H. C. Yee, Dmitry V. Kotov & Björn Sjögreen. (2020). High Order Finite Difference Methods with Subcell Resolution for Stiff Multispecies Discontinuity Capturing. Communications in Computational Physics. 17 (2). 317-336. doi:10.4208/cicp.250214.130814a
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