Implicit schemes for numerical simulations of hypersonic nonequilibrium flows

For the simulation of nonequilibrium flows past hypersonic re-entry vehicle, the two forms of the implicit total variation diminishing (TVD) schemes were proposed, which are derived from the diagonal form of the approximate-factorization algorithm and lower-upper (LU) decomposition scheme applied to the implicit part of Harten-Yee's TVD scheme, respectively. The numerical tests were taken for the two-dimensional and three-dimensional chemically nonequilibrium flows, and the results have demonstrated that the algorithms are efficient with high resolution and less cost in computation.