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Carsten Werner Schulz-Rinne

Bio: Carsten Werner Schulz-Rinne is an academic researcher. The author has contributed to research in topics: Rarefaction & Polytropic process. The author has an hindex of 2, co-authored 2 publications receiving 329 citations.

Papers
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TL;DR: The Riemann problem for two-dimensional gas dynamics with isentropic or polytropic gas is considered and the required relations for the initial data and the symmetry properties of the solutions are given.
Abstract: The Riemann problem for two-dimensional gas dynamics with isentropic or polytropic gas is considered. The initial data is constant in each quadrant and chosen so that only a rarefaction wave, shock wave, or slip line connects two neighboring constant initial states. With this restriction sixteen (respectively, fifteen) genuinely different wave combinations for isentropic (respectively, polytropic) gas exist. For each configuration the numerical solution is analyzed and illustrated by contour plots. Additionally, the required relations for the initial data and the symmetry properties of the solutions are given. The chosen calculations correspond closely to the cases studied by T. Zhang and Y. Zheng [SIAM J. Math. Anal., 21 (1990), pp. 593–630], so that the analytical theory can be directly compared to our numerical study.

355 citations

DOI
01 Jan 1992
TL;DR: In this paper, the authors considered the Riemann problem for two-dimensional gas dynamics with isentropic or polytropic gas, where the initial data is constant in each quadrant and chosen so that only a rarefaction wave, shock wave, or slip line connects two neighboring constant initial states.
Abstract: The Riemann problem for two-dimensional gas dynamics with isentropic or polytropic gas is considered. The initial data is constant in each quadrant and chosen so that only a rarefaction wave, shock wave, or slip line connects two neighboring constant initial states. With this restriction sixteen (respectively, fifteen) genuinely different wave combinations for isentropic (respectively, polytropic) gas exist. For each configuration the numerical solution is analyzed and illustrated by contour plots. Additionally, the required relations for the initial data and the symmetry properties of the solutions are given. The chosen calculations correspond closely to the cases studied by T. Zhang and Y. Zheng [SIAM J. Math. Anal., 21 (1990), pp. 593–630], so that the analytical theory can be directly compared to our numerical study.

48 citations


Cited by
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Journal ArticleDOI
TL;DR: A class of high resolution multidimensional wave-propagation algorithms is described for general time-dependent hyperbolic systems based on solving Riemann problems and applying limiter functions to the resulting waves, which are then propagated in a multiddimensional manner.

516 citations

Journal ArticleDOI
TL;DR: This paper uses positive schemes to solve Riemann problems for two-dimensional gas dynamics to show how well the positivity principle works.
Abstract: The positivity principle and positive schemes to solve multidimensional hyperbolic systems of conservation laws have been introduced in [X.-D. Liu and P. D. Lax, J. Fluid Dynam., 5 (1996), pp. 133--156]. Some numerical experiments presented there show how well the method works. In this paper we use positive schemes to solve Riemann problems for two-dimensional gas dynamics.

471 citations

Journal ArticleDOI
TL;DR: In this paper, a specific energy equation instead of the thermal energy equation is used to handle shocks in smooth particle hydrodynamics (SPH) and the resulting equations are very similar to the equations constructed for Riemann solutions of compressible gas dynamics.

397 citations

Journal ArticleDOI
TL;DR: The results of computations with eight explicit finite difference schemes on a suite of one-dimensional and two-dimensional test problems for the Euler equations are presented in various formats.
Abstract: The results of computations with eight explicit finite difference schemes on a suite of one-dimensional and two-dimensional test problems for the Euler equations are presented in various formats. Both dimensionally split and two-dimensional schemes are represented, as are central and upwind-biased methods, and all are at least second-order accurate.

365 citations

Journal ArticleDOI
TL;DR: In this article, the Riemann-solvers-free central scheme was used to solve the 2D case of the Euler problem for the Com- pressible Euler equations.
Abstract: We report here on our numerical study of the two-dimensional Riemann problem for the com- pressible Euler equations. Compared with the relatively simple 1-D congurations, the 2-D case consists of a plethora of geometric wave patterns which pose a computational challenge for high- resolution methods. The main feature in the present computations of these 2-D waves is the use of the Riemann-solvers-free central schemes presented in (11). This family of central schemes avoids the intricate and time-consuming computation of the eigensystem of the problem, and hence oers a considerably simpler alternative to upwind methods. The numerical results illustrate that despite their simplicity, the central schemes are able to recover with comparable high-resolution, the various features observed in the earlier, more expensive computations. AMS subject classication: Primary 65M10; Secondary 65M05

339 citations