TIME INTEGRATION ALGORITHMS FOR THE 2-DIMENSIONAL EULER EQUATIONS ON UNSTRUCTURED MESHES

Explicit and implicit time integration algorithms for the two-dimensio nal Euler equations on unstructured grids are presented. Both cell-cen tered and cell-vertex finite volume upwind schemes utilizing Roe's app roximate Riemann solver are developed. For the cell-vertex scheme, a f our-stage Runge-Kutta time integration, a four-stage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method, and two methods utilizing precon ditioned sparse matrix solvers are presented. For the cell-centered sc heme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) dec omposition, and a hybrid scheme utilizing both Runge-Kutta and LU meth ods are presented. A reverse Cuthill-McKee renumbering scheme is emplo yed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration sch emes is made for both first-order and higher order accurate solutions using several mesh sizes. higher order accuracy is achieved by using m ultidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the pr econditioned sparse matrix solvers perform better than the other metho ds as the number of elements in the mesh increases.