Characteristic local discontinuous Galerkin methods for solving time-dependent convection-dominated Navier-Stokes equations

摘要

Combining the characteristic method and the local discontinuous Galerkinmethod with carefully constructing numerical fluxes, we design the variationalformulations for the time-dependent convection-dominated Navier-Stokesequations in $\mathbb{R}^2$. The proposed symmetric variational formulation isstrictly proved to be unconditionally stable; and the scheme has the strikingbenefit that the conditional number of the matrix of the corresponding matrixequation does not increase with the refining of the meshes. The presentedscheme works well for a wide range of Reynolds numbers, e.g., the scheme stillhas good error convergence when $Re=0.5 e+005$ or $1.0 e+ 008$. Extensivenumerical experiments are performed to show the optimal convergence orders andthe contours of the solutions of the equation with given initial and boundaryconditions.