Abstract

Many complex nonlinear systems have intrinsic structures such as energy dissipation or conservation, and/or positivity/bound preserving. It is desirable, sometimes necessary, to preserve these structures in a numerical scheme. I will present a new SAV approach which allows us to construct high-order, linear, decoupled energy stable schemes, which can also be positivity/bound preserving, for a large class of dissipative systems. It particular, I will present new high-order SAV schemes for Navier-Stokes equations which allow us to obtain high-order error estimates and new simulation results which were difficult to obtain (with similar computational resource) using previous schemes.