Boundary Conditions for Semi-Lagrangian Schemes: Testing Some Alternatives in One-Dimensional Models

Abstract

The one-dimensional advection equation and the one-dimensional advection adjustment equation with rotation are used as test beds for the design of well-posed boundary conditions for the initial-boundary-value problem using semi-Lagrangian discretization. Three options are found to be stable in experimental tests: trajectory truncation, time interpolation, and a well-posed buffer zone. Stability is proved for all three for the one-dimensional advection equation when linear interpolation is used for the interpolation associated with the semi-Lagrangian discretization.