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difficult part of creating a finite-volume scheme for MHD is the determination of the hyperbolic fluxes at each cell A new implicit algorithm is developed for solving the time-dependent , nonideal magnetohydrodynamic equations. It can also be used interface. Approximate Riemann solvers are a class of as an efficient relaxation scheme for steady state… (More)

- John Loverich, Uri Shumlak
- Computer Physics Communications
- 2005

A discontinuous Galerkin method for the full two-fluid plasma model is described. The plasma model includes complete electron and ion fluids, which allows charge separation, separate electron and ion temperatures and velocities. Complete Maxwell's equations are used including displacement current. The algorithm is validated by benchmarking against existing… (More)

A discontinuous Galerkin method for the ideal 5 moment two-fluid plasma system is presented. The method uses a second or third order discontinuous Galerkin spatial discretization and a third order TVD Runge-Kutta time stepping scheme. The method is benchmarked against an analytic solution of a dispersive electron acoustic square pulse as well as the… (More)

- Ammar Hakim, John Loverich, Uri Shumlak
- J. Comput. Physics
- 2006

Algorithms for the solution of the five-moment ideal Two-Fluid equations are presented. The ideal Two-Fluid model is more general than the often used magnetohydrodynamic (MHD) model. The model takes into account electron inertia effects, charge separation and the full electromagnetic field equations and allows for separate electron and ion motion. The… (More)

- E. T. Meier, A. H. Glasser, V. S. Lukin, Uri Shumlak
- J. Comput. Physics
- 2012

- Uri Shumlak, R. Lilly, N. Reddell, E. Sousa, B. Srinivasan
- Computer Physics Communications
- 2011

The multi-fluid plasma model only assumes local thermodynamic equilibrium within each fluid, e.g. ion and electron fluids for the two-fluid plasma model. Derivation of the MHD model involves several asymptotic and simplifying assumptions that can limit its applicability. Therefore, the two-fluid plasma model more accurately represents the appropriate… (More)

- W. Lowrie, V. S. Lukin, Uri Shumlak
- J. Comput. Physics
- 2011

- G. V. Vogman, Phillip Colella, Uri Shumlak
- J. Comput. Physics
- 2014

- E. Kansa, Uri Shumlak, Semyon Tsynkov
- J. Comput. Physics
- 2013

Keywords: Field reversed configuration (FRC) Single fluid magnetohydrodynamics (MHD) Quasi-static magnetic field Artificial boundary condition (ABC) The method of difference potentials Calderon's potentials and projections Boundary equations with projections a b s t r a c t Confining dense plasma in a field reversed configuration (FRC) is considered a… (More)

- E. T. Meier, V. S. Lukin, Uri Shumlak
- Computer Physics Communications
- 2010

a r t i c l e i n f o a b s t r a c t This paper describes a study of the effects of the overall spatial resolution, polynomial degree and computational grid directionality on the accuracy of numerical solutions of a highly anisotropic thermal diffusion equation using the spectral element spatial discretization method. The high-order spectral element… (More)