Adaptive finite-volume WENO schemes on dynamically redistributed grids for compressible Euler equations

Pathak, Harshavardhana S and Shukla, Ratnesh K (2016) Adaptive finite-volume WENO schemes on dynamically redistributed grids for compressible Euler equations. In: JOURNAL OF COMPUTATIONAL PHYSICS, 319 . pp. 200-230.

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Abstract

A high-order adaptive finite-volume method is presented for simulating inviscid compressible flows on time-dependent redistributed grids. The method achieves dynamic adaptation through a combination of time-dependent mesh node clustering in regions characterized by strong solution gradients and an optimal selection of the order of accuracy and the associated reconstruction stencil in a conservative finite-volume framework. This combined approach maximizes spatial resolution in discontinuous regions that require low-order approximations for oscillation-free shock capturing. Over smooth regions, high-order discretization through finite-volume WENO schemes minimizes numerical dissipation and provides excellent resolution of intricate flow features. The method including the moving mesh equations and the compressible flow solver is formulated entirely on a transformed time-independent computational domain discretized using a simple uniform Cartesian mesh. Approximations for the metric terms that enforce discrete geometric conservation law while preserving the fourth-order accuracy of the two-point Gaussian quadrature rule are developed. Spurious Cartesian grid induced shock instabilities such as carbuncles that feature in a local one-dimensional contact capturing treatment along the cell face normals are effectively eliminated through upwind flux calculation using a rotated Hartex-Lax-van Leercontact resolving (HLLC) approximate Riemann solver for the Euler equations in generalized coordinates. Numerical experiments with the fifth and ninth-order WENO reconstructions at the two-point Gaussian quadrature nodes, over a range of challenging test cases, indicate that the redistributed mesh effectively adapts to the dynamic flow gradients thereby improving the solution accuracy substantially even when the initial starting mesh is non-adaptive. The high adaptivity combined with the fifth and especially the ninth-order WENO reconstruction allows remarkably sharp capture of discontinuous propagating shocks with simultaneous resolution of smooth yet complex small scale unsteady flow features to an exceptional detail. (C) 2016 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Publication:	JOURNAL OF COMPUTATIONAL PHYSICS
Publisher:	ACADEMIC PRESS INC ELSEVIER SCIENCE
Additional Information:	Copy right for this article belongs to the ACADEMIC PRESS INC ELSEVIER SCIENCE, 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA
Keywords:	Compressible flows; WENO; Moving mesh method; Adaptive mesh redistribution; Finite-volume method
Department/Centre:	Division of Mechanical Sciences > Mechanical Engineering
Date Deposited:	30 Jun 2016 05:50
Last Modified:	30 Jun 2016 05:50
URI:	http://eprints.iisc.ac.in/id/eprint/54072

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