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The Delta x B = 0 Constraint Versus Minimization of Numerical Errors in MHD SimulationsThe MHD equations are a system of non-strictly hyperbolic conservation laws. The non-convexity of the inviscid flux vector resulted in corresponding Jacobian matrices with undesirable properties. It has previously been shown by Powell et al. (1995) that an 'almost' equivalent MHD system in non-conservative form can be derived. This non-conservative system has a better conditioned eigensystem. Aside from Powell et al., the MHD equations can be derived from basic principles in either conservative or non-conservative form. The Delta x B = 0 constraint of the MHD equations is only an initial condition constraint, it is very different from the incompressible Navier-Stokes equations in which the divergence condition is needed to close the system (i.e., to have the same number of equations and the same number of unknown). In the MHD formulations, if Delta x B = 0 initially, all one needs is to construct appropriate numerical schemes that preserve this constraint at later time evolutions. In other words, one does not need the Delta x B condition to close the MHD system. We formulate our new scheme together with the Cargo & Gallice (1997) form of the MHD approximate Riemann solver in curvilinear grids for both versions of the MHD equations. A novel feature of our new method is that the well-conditioned eigen-decomposition of the non-conservative MHD equations is used to solve the conservative equations. This new feature of the method provides well-conditioned eigenvectors for the conservative formulation, so that correct wave speeds for discontinuities are assured. The justification for using the non-conservative eigen-decomposition to solve the conservative equations is that our scheme has a better control of the numerical error associated with the divergence of the magnetic condition. Consequently, computing both forms of the equations with the same eigen-decomposition is almost equivalent. It will be shown that this approach, using the non-conservative eigensystem when solving the conservative equations, also works well in the context of standard shock-capturing schemes.
Document ID
20030014501
Acquisition Source
Ames Research Center
Document Type
Conference Paper
Authors
Yee, H. C.
(NASA Ames Research Center Moffett Field, CA United States)
Sjoegreen, Bjoern
(Royal Inst. of Tech. Sweden)
Mansour, Nagi
Date Acquired
August 21, 2013
Publication Date
November 15, 2002
Subject Category
Plasma Physics
Meeting Information
Meeting: 5th International Congress of Industrial and Applied Mathematics
Location: Sydney
Country: Australia
Start Date: July 7, 2003
End Date: July 11, 2003
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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