Method of lines and direct discretization: A comparison for linear advection
Two related schemes are compared for two-dimensional linear advection: a scheme based on dimension splitting starting from fully discrete one- dimensional discretization, and a scheme based on the method of lines. Both schemes use the same four-point upwind biased stencil in each direction and both are considered with flux limiting to avoid oscillations and negative values of the solution. Theoretical aspects of the application of the methods for 2-D models involving error analysis and computational cost are discussed. Numerical tests are run on uniform grids with local uniform grid refinement to compare their accuracy and computational efficiency.
scientific article; zbMATH DE number 550352
scientific article