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Finite volume WLSQR scheme and its applications to transonic flows

Fürst, Jiří — 2006

Programs and Algorithms of Numerical Mathematics

This article describes the development of a high order numerical method for the solution of compressible transonic flows. The discretisation in space is based on the standard finite volume method of Godunov's type. A higher order of accuracy is achieved by a piecewise polynomial interpolation similar to the ENO or weighted ENO methods (see e.g. [8].

An unsteady numerical solution of viscous compressible flows in a channel

Punčochářová, PetraKozel, KarelFürst, JiříHoráček, Jaromír — 2006

Programs and Algorithms of Numerical Mathematics

The work deals with numerical solution of unsteady flows in a 2D channel where one part of the channel wall is changing as a given function of time. The flow is described by the system of Navier-Stokes equations for compressible (laminar) flows. The flow has low velocities (low Mach numbers) and is numerically solved by the finite volume method. Moving grid of quadrilateral cells is considered in the form of conservation laws using ALE (Arbitrary Lagrangian-Eulerian) method.

High order finite volume schemes for numerical solution of 2D and 3D transonic flows

Jiří FürstKarel KozelPetr Furmánek — 2009

Kybernetika

The aim of this article is a qualitative analysis of two modern finite volume (FVM) schemes. First one is the so called Modified Causon’s scheme, which is based on the classical MacCormack FVM scheme in total variation diminishing (TVD) form, but is simplified in such a way that the demands on computational power are much smaller without loss of accuracy. Second one is implicit WLSQR (Weighted Least Square Reconstruction) scheme combined with various types of numerical fluxes (AUSMPW+ and HLLC)....

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