MUSCL and THINC hybrid scheme for strong and very weak shock waves in steady and unsteady flows
ORAL
Abstract
The monotonic upstream-centered schemes for conservation laws (MUSCL) are widely used to obtain second-order accuracy in finite volume methods [1]. Although the fundamental flow can be computed by MUSCL, it is known that MUSCL is too dissipative to solve a density discontinuity [2,3]. In addition, a recent study by the authors found that MUSCL cannot solve weak shock waves due to the excessive dissipation [4]. To overcome the problem, we focused on the tangent of hyperbola interface capturing (THINC) technique and found that the hybrid MUSCL-THINC scheme [5], which was developed for two-phase flow computations, can sharply capture weak shock waves [6]. This scheme was also valid for some unsteady compressible flows. However, the hybrid MUSCL-THINC scheme showed oscillations behind strong stationary shock waves, and the convergence was very poor in steady problems. In this study, we modified the weighting strategy of the cell boundary values computed by MUSCL and THINC to avoid the excessive usage of THINC around strong shocks. As a result, the modified scheme showed better convergence in the steady, two-dimensional, blunt-body problem with M = 3.0. We confirmed that the modification did not significantly affect high-resolution density discontinuity and weak shock capturing in unsteady problems. With this modification, high-resolution and robust computation was firstly achieved in the MUSCL and THINC hybrid scheme.
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Publication: [1] B. van Leer, Towards the Ultimate Conservative Difference Scheme. V. A Second-Order Sequel to Godunov's Method, J. Comput. Phys. 32, 101 (1979).<br>[2] T. Nonomura, K. Kitamura, and K. Fujii, A Simple Interface Sharpening Technique with a Hyperbolic Tangent Function Applied to Compressible Two-Fluid Modeling, J. Comput. Phys. 258, 95 (2014).<br>[3] X. Deng, B. Xie, R. Loubère, Y. Shimizu, and F. Xiao, Limiter-Free Discontinuity-Capturing Scheme for Compressible Gas Dynamics with Reactive Fronts, Comput. Fluids 171, 1 (2018).<br>[4] G. Fukushima, K. Kitamura, and A. Sasoh, On Peculiar Behaviors of Captured Very-Weak Moving Shockwaves, in AIAA AVIATION 2022 Forum (American Institute of Aeronautics and Astronautics, 2022).<br>[5] T.-Y. Chiu, Y.-Y. Niu, and Y.-J. Chou, Accurate Hybrid AUSMD Type Flux Algorithm with Generalized Discontinuity Sharpening Reconstruction for Two-Fluid Modeling, J. Comput. Phys. 443, 110540 (2021).<br>[6] G. Fukushima, K. Kitamura, and A. Sasoh, Improvement of Very Weak Shock Capturing Using Hybrid MUSCL-THINC, in The 34th International Symposium on Shock Waves (2023)
