METHOD OF LINES AND DIRECT DISCRETIZATION - A COMPARISON FOR LINEAR ADVECTION

In this paper two related schemes are compared for two-dimensional lin ear advection: a scheme based on dimension splitting starting from a f ully discrete one-dimensional discretization, and a scheme based on th e 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 in the solutions. Along wit h a theoretical discussion, we also give some numerical test results, on uniform grids and with local uniform grid refinement, to compare th e accuracy and computational efficiency.