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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 10, Pages 1627–1639 (Mi zvmmf10790)  

Numerical solution of test problems using a modified Godunov scheme

Yu. V. Tunik

Research Institute of Mechanics, Moscow State University, Moscow, Russia

Abstract: Modifications of Godunov’s scheme based on V.P. Kolgan’s approach to the construction of second-order accurate schemes in space for smooth solutions are proposed. The gasdynamic parameters linearly interpolated in a mesh cell, but the Riemann problem is solved for parameters at an intermediate point between the center and the boundary of the cell. Properties of Kolgan’s scheme and the proposed modifications, such as monotonicity and entropy nondecrease, are examined as applied to the system of differential equations describing plane sound waves propagation in a resting gas. Test problems in nonlinear gas dynamics are solved, namely, the Riemann problem in a pipe, transformation of an inhomogeneity in a plane-parallel flow, supersonic flow entering an axisymmetric convergent-divergent nozzle with a coaxial central body, and coaxial supersonic flow around a cylinder. The efficiency of schemes with an intermediate point is demonstrated.

Key words: numerical scheme, monotonicity of schemes, entropy nondecrease, order of accuracy, difference analogue, numerical grid, sound waves, test problems, Euler equations, invariants, inviscid ideal gas, convergent-divergent nozzle, central body.

DOI: https://doi.org/10.31857/S004446690003583-2

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English version:
Computational Mathematics and Mathematical Physics, 2018, 58:10, 1573–1584

Bibliographic databases:

UDC: 519.635
Received: 11.05.2017

Citation: Yu. V. Tunik, “Numerical solution of test problems using a modified Godunov scheme”, Zh. Vychisl. Mat. Mat. Fiz., 58:10 (2018), 1627–1639; Comput. Math. Math. Phys., 58:10 (2018), 1573–1584

Citation in format AMSBIB
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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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