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760
Multidimensional shock interaction for a Chaplygin gas
, 2008
"... A Chaplygin gas is an inviscid, compressible fluid in which the acoustic fields are linearly degenerate. We analyse the multidimensional shocks, which turn out to be sonic. Two shocks in general position interact rather simply. We investigate several twodimensional Riemann problems and prove the e ..."
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Cited by 10 (0 self)
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A Chaplygin gas is an inviscid, compressible fluid in which the acoustic fields are linearly degenerate. We analyse the multidimensional shocks, which turn out to be sonic. Two shocks in general position interact rather simply. We investigate several twodimensional Riemann problems and prove
Solution of twodimensional Riemann problems for gas dynamics without Riemann problem solvers
 Numer. Methods Partial Differential Equations
, 2002
"... We report here on our numerical study of the twodimensional Riemann problem for the compressible Euler equations. Compared with the relatively simple 1D configurations, the 2D case consists of a plethora of geometric wave patterns that pose a computational challenge for highresolution methods. T ..."
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Cited by 44 (4 self)
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We report here on our numerical study of the twodimensional Riemann problem for the compressible Euler equations. Compared with the relatively simple 1D configurations, the 2D case consists of a plethora of geometric wave patterns that pose a computational challenge for highresolution methods
Solution of Two Dimensional Riemann Problem of Gas Dynamics by Positive Schemes
 SIAM J. Sci. Comput
, 1995
"... The positivity principle and positive schemes to solve multidimensional hyperbolic systems of conservation laws have been introduced in [8]. Some numerical experiments presented there show how well the method works. In this paper we use positive schemes to solve Riemann problems for twodimensional ..."
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Cited by 51 (1 self)
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The positivity principle and positive schemes to solve multidimensional hyperbolic systems of conservation laws have been introduced in [8]. Some numerical experiments presented there show how well the method works. In this paper we use positive schemes to solve Riemann problems for twodimensional
TwoDimensional Riemann Problems for the Compressible Euler System∗∗
"... Abstract Riemann problems for the compressible Euler system in two space dimensions are complicated and difficult, but a viable alternative remains missing. We list merits of onedimensional Riemann problems and compare them with those for the current twodimensional Riemann problems, to illustrat ..."
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Abstract Riemann problems for the compressible Euler system in two space dimensions are complicated and difficult, but a viable alternative remains missing. We list merits of onedimensional Riemann problems and compare them with those for the current twodimensional Riemann problems
Riemann Problems for TwoDimensional UTSD Riemann Problems for the TwoDimensional Unsteady Transonic Small Disturbance Equation
"... Abstract. We study a twoparameter family of Riemann problems for the UTSD equation, also called the twodimensional Burgers equation, which is used to model the transition from regular to Mach reflection for weak shock waves. The related initialvalue problem consists of oblique shock data in the u ..."
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Abstract. We study a twoparameter family of Riemann problems for the UTSD equation, also called the twodimensional Burgers equation, which is used to model the transition from regular to Mach reflection for weak shock waves. The related initialvalue problem consists of oblique shock data
Riemann Problems for the TwoDimensional Unsteady Transonic Small Disturbance Equation
"... We study a twoparameter family of Riemann problems for the UTSD equation, also called the twodimensional Burgers equation, which is used to model the transition from regular to Mach reflection for weak shock waves. The related initialvalue problem consists of oblique shock data in the upper h ..."
Abstract

Cited by 3 (2 self)
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We study a twoparameter family of Riemann problems for the UTSD equation, also called the twodimensional Burgers equation, which is used to model the transition from regular to Mach reflection for weak shock waves. The related initialvalue problem consists of oblique shock data in the upper
QuasiOneDimensional Riemann Problems and Their Role in SelfSimilar TwoDimensional Problems
, 1998
"... We study twodimensional Riemann problems with piecewise constant data. We identify a class of twodimensional systems, including many standard equations of compressible flow, which are simplified by a transformation to similarity variables. For equations in this class, a twodimensional Riemann prob ..."
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Cited by 20 (10 self)
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We study twodimensional Riemann problems with piecewise constant data. We identify a class of twodimensional systems, including many standard equations of compressible flow, which are simplified by a transformation to similarity variables. For equations in this class, a twodimensional Riemann
Periodic Structure in TwoDimensional Riemann Problems for HamiltonJacobi Equations
, 1998
"... This paper investigates the structure of twodimensional Riemann problems for HamiltonJacobi equations. We show that it is possible for the viscosity solution to contain closed characteristic orbits, enclosing furthermore a periodic sonic structure, which in turn encloses a parabolic structure. The ..."
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This paper investigates the structure of twodimensional Riemann problems for HamiltonJacobi equations. We show that it is possible for the viscosity solution to contain closed characteristic orbits, enclosing furthermore a periodic sonic structure, which in turn encloses a parabolic structure
Lattice Coulomb gas representations of twodimensional problems
 J. Phys. A
, 1978
"... content has been downloaded from IOPscience. Please scroll down to see the full text. ..."
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Cited by 6 (0 self)
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content has been downloaded from IOPscience. Please scroll down to see the full text.
An Approximate Riemann Solver for Magnetohydrodynamics
, 1994
"... An approximate Riemann solver is developed for the governing equations of ideal magnetohydrodynamics (MHD). The Riemann solver has an eightwave structure, where seven of the waves are those used in previous work on upwind schemes for MHD, and the eighth wave is related to the divergence of the magn ..."
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Cited by 65 (9 self)
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the use of staggered grids or a projection scheme, one or the other of which was necessary in previous work on upwind schemes for MHD. A test problem made up of a shock tube with rotated initial conditions is solved to show that the twodimensional code yields answers consistent with the onedimensional
Results 1  10
of
760