AbstractChemically reacting flows have many applications in combustion. There are several difficulties in constructing high-order numerical methods: (1) Due to the rapid reaction rate, the system may contain stiff source terms. (2) The transition points near the shocks may trigger the stiff source leading to spurious shock speed. (3) Physically, the density, internal energy are positive, and th...
AbstractIn this talk we consider the stochastic homogenization of elliptic non-divergence form equations on the integer lattice and the corresponding model of random walks in random environment (RWRE) which is a martingale. We will derive the optimal rates of the homogenization for the Dirichlet problem. We will also discuss the correlation structure of the invariant measure and quantitative es...