Conservative and orthogonal discretization for the Lorentz force.
In the case of errors in the computation of \(\nabla\cdot B\), the Lorentz force \(J\times B\) should be discretized in such a way that it is orthogonal to the magnetic field \(B\) (here \(J=\nabla\times B\)). Many magnetohydrodynamic (MHD) codes follow this approach. Unfortunately, such discretizations are not conservative in general. The author shows that it is possible to construct a conservative scheme in which the discretized Lorentz force is orthogonal to the magnetic field in the cell centers. This note does not try to evaluate the accuracy of such discretization. Although the discussion is restricted to two-dimensional Cartesian grids, the author claims that it could be trivially extended to three-dimensional grids. There is no attempt of a generalization to non-Cartesian or unstructured grids.
scientific article; zbMATH DE number 1901691