On the application of a variant CE/SE method for solving two-dimensional ideal MHD equations

In this article we implement a variant space–time conservation element and solution element (CE/SE) method for the numerical solution of two-dimensional ideal magnetohydrodynamic (MHD) equations. The current method uses regular rectangular mesh elements for the domain discretization in two space dimensions. In the method, a single conservation element at each grid point is employed for solving conservation laws no matter in one, two, and three space dimensions. The present scheme uses the conservation element to calculate flow variables only, while the gradients of flow variables are calculated by a central differencing reconstruction procedure. Although the present scheme does not satisfy the divergence free condition, the numerical results obtained with and without divergence cleaning procedure are almost similar. Several two-dimensional test cases are included in this manuscript. These problems are hard test cases for those numerical methods which do not satisfy the divergence free condition. Therefore, the test problems further verify the performance of proposed scheme. A comparison with central schemes shows better resolution of the CE/SE method results.