Numerical Solution of Euler equations using TVD scheme

One and two-dimensional Euler equations were solved by finite volume method using a TVD(total variation diminishing) scheme proposed by Chakravarthy. For two-dimensional Euler equations, curvilinear coordinates were used. An approximate factorization approach was used in two-dimensional implicit formulation. The block matrix equations were transformed into separated algebraic equations. Thus computer time needed for solving the equations was reduced. Several two-dimensional examples were given here. The numerical results show that the method is time-saving indeed and in good agreement with Jameson's results. The results also show that the good shock capturing ability and high shock resolutions of TVD scheme are retained .