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- Farzad Ismail, Philip L. Roe
- J. Comput. Physics
- 2009

- Rémi Abgrall, Philip L. Roe
- J. Sci. Comput.
- 2003

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 have mostly been developed in the context of triangular or tetrahedral elements whose degrees of freedom are their nodal values. We work here with more general… (More)

This paper presents a computational scheme for compressible magnetohydrody-namics (MHD). The scheme is based on the same elements that make up many modern compressible gas dynamics codes: a high-resolution upwinding based on an approximate Riemann solver for MHD and limited reconstruction; an optimally smoothing multi-stage time-stepping scheme; and… (More)

This paper reports progress towards high-order fluctuation-splitting schemes for the Navier-Stokes Equations. High-order schemes we examined previously are all based on gradient reconstruction, which may result in undesired mesh-dependency problem due to the somewhat ambiguous gradient reconstruction procedures. Here, we consider schemes for P2 elements in… (More)

- K. W. Morton, Philip L. Roe
- SIAM J. Scientific Computing
- 2001

- Jose G. Vasconcelos, Steven J. Wright, Philip L. Roe
- 2005

Operational problems and system damage have been linked to the flow regime transition between free surface and pressurized flow in rapidly filling stormwater and combined sewer systems. In response, emphasis has been placed on the development of numerical models to describe hydraulic bores and other flow phenomena that may occur in these systems. Current… (More)

Shock-capturing finite volume schemes often give rise to anomalous results in hypersonic flow. We present a wide-ranging survey of numerical experiments from 12 different flux functions in one-and two-dimensional contexts. Included is a recently developed function that satisfies the second law of thermodynamics. It is found here that there are at least two… (More)

- V Venkatakrishnan, H D Simon, +111 authors Newton-Krylov-Schwarz
- 1995

Adapted hybrid prismatic-tetrahedral grid about a hemisphere. (b) Surface Mach contours on the symmetry plane for supersonic laminar ow (M 1 = 1:4, Re = 1000) 128]. 37 Figure 8. Comparison of various discretization methods for the circular advection problem 13]. (a) Grid used for the two-dimensional advection equation. (b) Piecewise-constant nite-volume… (More)

- Philip L. Roe, Dinshaw S. Balsara
- SIAM Journal of Applied Mathematics
- 1996

- H L Decougny, K D Devine, +28 authors S Y Lin
- 1998

order accurate discontinuous discontinuous nite element solution of the 2D Euler equations, A massively parallel adaptive nite element method with dynamic load balancing, SAND 93-0936C (1993). 21. K. Eriksson and C. Johnson, Adaptive nite element methods for parabolic problems I: A linear model problem, SIAM J. Adaptive nite element methods for parabolic… (More)