• Publications
  • Influence
Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes
  • P. Roe
  • Mathematics
  • 1 August 1997
Several numerical schemes for the solution of hyperbolic conservation laws are based on exploiting the information obtained by considering a sequence of Riemann problems. It is argued that inExpand
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Regular Article: A Solution-Adaptive Upwind Scheme for Ideal Magnetohydrodynamics
This paper presents a computational scheme for compressible magnetohydrodynamics (MHD). The scheme is based on the same elements that make up many modern compressible gas dynamics codes: aExpand
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On Godunov-type methods near low densities
Abstract When the energy of a flow is largely kinetic, many conservative differencing schemes may fail by predicting non-physical states with negative density or internal energy. We describe asExpand
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CHARACTERISTIC-BASED SCHEMES FOR THE EULER EQUATIONS
P. L. RoeCollege of Aeronautics, Cranfield Institute of Technology,Cranfield MK43 0AL, EnglandIntroductionComputer simulations of fluid flow provide today the sort of detailedinformation concerningExpand
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Affordable, entropy-consistent Euler flux functions II: Entropy production at shocks
  • F. Ismail, P. Roe
  • Mathematics, Computer Science
  • J. Comput. Phys.
  • 1 August 2009
In this paper, an entropy-consistent flux is developed, continuing from the work of the previous paper. To achieve entropy consistency, a second and third-order differential terms are added to theExpand
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Some contributions to the modelling of discontinuous flows
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High Order Fluctuation Schemes on Triangular Meshes
We develop a new class of schemes for the numerical solution of first-order steady conservation laws. The schemes are of the residual distribution, or fluctuation-splitting type. These schemes haveExpand
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Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics
This paper explores a possible technique for extending to multidimensional flows some of the upwind-differencing methods that have proved highly successful in the one-dimensional case. Attention hereExpand
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Some Contributions to the Modeling of Discontinuous Flows
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A Well-Behaved TVD Limiter for High-Resolution Calculations of Unsteady Flow
A total variation diminishing (TVD) limiter is proposed that attempts to maximize performance given that the inherent limitation of TVD formulations is peak loss. For the scalar advection andExpand
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