Abstract: An explicit second-order upwind TVD scheme by H.C.Yee is first suc-cessfully extended to solve the viscous,diffussive,nonequilibrium,ionizing,hypersonic flowfields over a hemi-sphere.The governing gas-dynamic and species-continuity equations forlaminar flow are presented.The gas-dynamics/species continuity equations fully couplingprocedure is described in detail.Before this only the firstorder scheme and loosely coupledmethod was successfully used in this research field.The gais model for chemically relaxin...