Past Event: Oden Institute Seminar

Eulerian-Lagrangian Finite Volume Schemes for Linear Advection Problems

Todd Arbogast, Math, UT Austin

Abstract

Our objective is to simulate transport processes over very long time periods, as needed in, e.g., the simulation of geologic carbon sequestration. A good numerical method would be locally mass conservative, produce no or minimal over/under-shoots, produce minimal numerical diffusion, and require no CFL time-step limit for stability. The latter would allow better use of parallel computers, since time-stepping is essentially a serial process. Moreover, it would be good for the method to be of high order accuracy. Our approach is to develop Eulerian-Lagrangian methods, since they have the potential to attain the desired properties. We discuss our work on obtaining local mass and volume conservation in Eulerian-Lagrangian methods, resulting in a fully conservative method that achieves all of our desired properties except that the method is only formally second order. Numerical results and theoretical considerations are discussed. We then turn to more recent work on developing a formally higher order Eulerian-Lagrangian method using ideas from WENO schemes (resulting in an EL-WENO method).