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Current Density Conservative Scheme



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Available online at www sciencedirect com Journal of Computational Physics 227 2007 205 228 www elsevier com locate jcp A current density conservative scheme for incompressible MHD ows at a low magnetic Reynolds number Part II On an arbitrary collocated mesh Ming Jiu Ni a c Ramakanth Munipalli b Peter Huang b Neil B Morley a Mohamed A Abdou a a c MAE Department University of California at Los Angeles CA 90095 USA b HyperComp Inc Westlake Village CA 91362 USA Physics Department Graduate University of Chinese Academy of Sciences Beijing 100049 China Received 19 October 2006 received in revised form 16 April 2007 accepted 22 July 2007 Available online 8 August 2007 Abstract A conservative formulation of the Lorentz force is given here for magnetohydrodynamic MHD ows at a low magnetic Reynolds number with the current density calculated based on Ohm s law and the electrical potential formula This conservative formula shows that the total momentum contributed from the Lorentz force is conservative when the applied magnetic eld is constant For the case with a non constant applied magnetic eld the Lorentz force has been divided into two parts a strong globally conservative part and a weak locally conservative part The conservative formula has been employed to develop a conservative scheme for the calculation of the Lorentz force on an unstructured collocated mesh Only the current density uxes on the cell faces which are calculated using a consistent scheme with good conservation are needed for the calculation of the Lorentz force Meanwhile a conservative interpolation technique is designed to get the current density at the cell center from the current density uxes on the cell faces This conservative interpolation can keep the current density at the cell center conservative which can be used to calculate the Lorentz force at the cell center with good accuracy The Lorentz force calculated from the conservative current at the cell center is equivalent to the Lorentz force from



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