Abstract: A computer-implemented method for performing simulation includes establishing a mesh of a physical domain with nodes. The nodes represent a discretized physical quantity. The method accesses one or more different algorithms for evolving the nodes through sequential time steps. The method determines a unique combination of parameter values for each algorithm. In some examples, the parameter values can control dissipation, dispersion, and overshoot for each algorithm, as well as whether each algorithm is implicit or explicit. In some examples, the method can select one or more subsets of the nodes, and/or identify one or more time increments. The method can evolve the nodes in time, optionally using different time increments for different nodes in the mesh, and/or optionally using different algorithms for different nodes in the mesh. The method can optionally identify if an algorithm has failed to converge to a solution, and can switch to a different algorithm.