Method of lines and direct discretization: A comparison for linear advection. (English) Zbl 0797.65067

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.


65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
35L15 Initial value problems for second-order hyperbolic equations
65Y20 Complexity and performance of numerical algorithms
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