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




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


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.

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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How to Cite

Кочарина А.Р., Чирков Д.В. MUSCL-Scheme of the Third Order of Accuracy on a Non-Uniform Structured Grid // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2023. 24. 386-407. doi 10.26089/NumMet.v24r427



Methods and algorithms of computational mathematics and their applications