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A Solution-Adaptive Upwind Scheme for Ideal Magnetohydrodynamics Kenneth G. Powell,∗ Philip L. Roe,∗ Timur J. Linde,∗ Tamas I. Gombosi,† and Darren L. De Zeeuw† ∗W. M. Keck Foundation CFD Laboratory, Department of Aerospace Engineering, University of Michigan, Ann Arbor, Michigan 48109-2140; and †Space Physics Research Laboratory, Department of Atmospheric,… (More)

- 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)

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

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

In this paper a relationship between two approaches towards construction of genuinely two-dimensional upwind advection schemes is established. One of these approaches is of tile control volume type applicable on structured cartesian meshes. It resulted (see [14], [15]) in the compact high resolution schemes capable of maintaining second order accuracy in… (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)

- 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 wideranging survey of numerical experiments from 12 different flux functions in oneand 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)

- Philip L. Roe, Mohit Arora
- 2005

In order to embark on the development of numerical schemes for stiff problems, we have studied a model of relaxing heat flow. To isolate those errors unavoidably associated with discretization, a method of characteristics is developed, containing three free parameters depending on the stiffness ratio. It is shown that such “decoupled” schemes do not take… (More)