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approximately assuming Beam and Warming bottom boundary boundary layer interaction BURATYNSKI LU IMPLICIT Buratynski's LU scheme cartesian grid central differences components Convergence Histories Courant number diagonal Difference Operators domain eigenvalues employed equa Euler equations EULER JACOBIANS Euler Solution explicit boundary conditions fictitious points finite volume method flow Flux Vector Splitting Fourier's law free-stream implicit operator implicit portion interac inviscid shock reflection iteration layer interaction problem leading edge left hand side LU factoring LU IMPLICIT SCHEME Mach number matrix maximum Courant MESH SIZE NX mesh spacing Navier-Stokes equations no-slip conditions non-dimensional non-singular number of cells number of space numerical smoothing terms optimum parameters plate surface pressure rection Reynolds number second grid system second-order-accurate Section shock waves shock-boundary layer interaction shown in Figure skin friction Solution of Scheme solving the Navier-Stokes Splitting Implicit scheme stability steady state solution sweep three-point backward time-level tion Vector Splitting Implicit vergence x-velocity Profiles y-direction