Asymptotic-preserving schemes for unsteady flow simulations

Asymptotic preserving schemes are proposed for numerical simulation of unsteady flows in the relaxation framework. Using a splitting operator to treat the transport and the collision terms separately, we reconstruct a stable and accurate method that converges uniformly to the correct equilibrium. This convergence is also ensured when the relaxation time is unresolved (asymptotic preserving). Numerical results and comparisons are shown for the multidimensional Euler system of gas dynamics.