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Simple and robust contact-discontinuity capturing central algorithms for high speed compressible flows

Kolluru, R and Venkata Raghavendra, N and Raghurama Rao, SV and Sekhar, GN (2022) Simple and robust contact-discontinuity capturing central algorithms for high speed compressible flows. In: Applied Mathematics and Computation, 414 .

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Official URL: https://doi.org/10.1016/j.amc.2021.126660


The nonlinear convection terms in the governing equations of compressible fluid flows are hyperbolic in nature and are nontrivial for modelling and numerical simulation. Many numerical methods have been developed in the last few decades for this purpose and are typically based on Riemann solvers, which are strongly dependent on the underlying eigen-structure of the governing equations. Objective of the present work is to develop simple algorithms which are not dependent on the eigen-structure and yet can tackle easily the hyperbolic parts. Central schemes with smart diffusion mechanisms are apt for this purpose. For fixing the numerical diffusion, the basic ideas of satisfying the Rankine-Hugoniot (RH) conditions along with generalized Riemann invariants are proposed. Two such interesting algorithms are presented, which capture grid-aligned steady contact discontinuities exactly and yet have sufficient numerical diffusion to avoid numerical shock instabilities. Both the algorithms presented are robust in avoiding shock instabilities, apart from being accurate in capturing contact discontinuities, do not need wave speed corrections and are independent of eigen-struture of the underlying hyperbolic parts of the systems.

Item Type: Journal Article
Publication: Applied Mathematics and Computation
Publisher: Elsevier Inc.
Additional Information: The copyright for this article belongs to the Elsevier Inc.
Keywords: Diffusion; Nonlinear equations; Numerical methods, Accurate contact discontinuity capturing; Central scheme; Compressible flow solver; Contact discontinuities; Discontinuity capturing; Eigen-structure independence; Eigenstructures; Flow solver; Generalized riemann invariant; Hugoniot; Jump conditions; Rankine; Rankine-hugoniot jump condition; Riemann invariants; Robust central scheme, Compressible flow
Department/Centre: Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited: 02 Jul 2022 04:37
Last Modified: 02 Jul 2022 04:37
URI: https://eprints.iisc.ac.in/id/eprint/74031

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