DOI: https://doi.org/10.26089/NumMet.v24r427

MUSCL-scheme of the third order of accuracy on a non-uniform structured grid

Authors

  • Alena R. Kocharina
  • Denis V. Chirkov

Keywords:

MUSCL-scheme
high-order reconstruction
non-uniform mesh
structured mesh
finite volume method
Navier-Stokes equations

Abstract

An upwind finite volume scheme with third-order MUSCL-reconstruction at the cell interface is extended to non-uniform structured grids. The order of approximation of the original MUSCL-scheme with reconstruction using constant coefficients and the modified MUSCL-scheme with coefficients dependent on the grid steps is investigated for 1D nonlinear transport equation. It is shown that the order of approximation depends on the type of non-uniform grid. The cases of a grid with a constant clustering law and an arbitrary non-uniform grid are considered. It is shown analytically and numerically, that the non-uniform MUSCL-scheme with coefficients depending on the grid spacing has the third order of approximation on a non-uniform grid with a constant clustering law and the second order on an arbitrary grid. It is also shown that the MUSCL-scheme with constant coefficients does not approximate the original equation at all on an arbitrary non-uniform grid. Non-uniform MUSCL-reconstruction is introduced into the numerical algorithm for calculating incompressible fluid flows. Higher accuracy of the proposed scheme is demonstrated for a 2D problem of the flow around a circular cylinder and for a 3D fluid flow in a hydraulic turbine.

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Published

2023-11-13

Issue

Vol. 24 (2023): Issue 4.

Section

Methods and algorithms of computational mathematics and their applications

Author Biographies

Alena R. Kocharina

Novosibirsk national research state university
Kutateladze Institute of Thermophysics of SB RAS
• Research Engineer

Denis V. Chirkov

Novosibirsk national research state university
Kutateladze Institute of Thermophysics of SB RAS
• Senior Researcher

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