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A Runge–Kutta discontinuous Galerkin method for the Euler equations

✍ Scribed by Huazhong Tang; Gerald Warnecke

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
548 KB
Volume
34
Category
Article
ISSN
0045-7930

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✦ Synopsis

This paper presents a Runge-Kutta discontinuous Galerkin (RKDG) method for the Euler equations of gas dynamics from the viewpoint of kinetic theory. Like the traditional gas-kinetic schemes, our proposed RKDG method does not need to use the characteristic decomposition or the Riemann solver in computing the numerical flux at the surface of the finite elements. The integral term containing the non-linear flux can be computed exactly at the microscopic level. A limiting procedure is carefully designed to suppress numerical oscillations. It is demonstrated by the numerical experiments that the proposed RKDG methods give higher resolution in solving problems with smooth solutions. Moreover, shock and contact discontinuities can be well captured by using the proposed methods.

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