Space-time residual distribution schemes for hyperbolic conservation laws on unstructured linear finite elements

Multidimensional upwind residual distribution schemes are extended to the context of continuous linear space–time finite elements for the time accurate solution of scalar and hyperbolic systems of conservation laws. The formulation leads to a consistent discretization of the space-time domain, thus retaining the properties of the underlying basic schemes both in space and time. We propose a particular space–time mesh configuration containing two layers of elements and three levels of nodes in time. This construction leads to unconditionally stable implicit time stepping while retaining second-order spatial and temporal accuracy in smooth flows and monotone solution across steep gradients. The presented schemes have a strong potential in the field of moving grids, since they allow a dynamic change of the space–time mesh geometry. Numerical results demonstrate the robustness, accuracy and monotonicity of the method. Copyright © 2002 John Wiley & Sons, Ltd.