Dr. Lisa Davis (Dept. of Mathematical Sciences, MSU)

02/17/2022    3:10pm

Abstract:

The focus of this talk is the development of a time filtering process for an explicit scheme for hyperbolic partial differential equations.  Recently the time filter has been combined with fully implicit schemes for nonlinear problems in order to increase accuracy with minimal modifications to existing (possibly legacy) code.  This has proven to be an inexpensive and simple approach to increasing accuracy for model simulations of complex systems.  It can be achieved by simply applying the time filter at each time step of the implicit method.  In this talk, we demonstrate that the filtering scheme can also be combined with explicit schemes for hyperbolic problems to increase accuracy.  A new explicit implementation is presented, and increased accuracy of the filtered upwind scheme is observed for test problems.  However, the typical treatments for explicit schemes for hyperbolic problems are still required.  That is, CFL conditions must be derived and enforced in order for the filtered scheme to remain stable. In the talk, we will give results for the filtered upwind scheme and compare it to the classical upwind scheme. A stability condition for the new algorithm is derived, and numerical computations illustrate stability and convergence of the filtered scheme.