Novel numerical techniques based upon Steger-Warming, Van Leer, and Roe-type flux splittings are presented in three-dimensional generalized coordinates for the Navier-Stokes equations governing flows out of chemical and thermal equilibrium. Attention is placed on convergence to steady-state solutions with fully coupled chemistry. Time integration schemes including explicit m-stage Runge-Kutta, implicit approximate-factorization, relaxation, and LU decomposition are investigated and compared in terms of residual reduction per unit of CPU time. Practical issues such as code vectorization and memory usage on modern supercomputers are discussed.
Two new methods are presented for solving the Euler equations using a compact higher order polynomial reconstruction technique on unstructured grids. The methods use a characteristic-based approach with a cell-centered finite volume method. For transonic Ringleb flow, computations are performed for first-order to fourth-order accuracy and are compared with the hodograph solution. Results for a 10-deg ramp case are also presented. An analysis is performed that demonstrates that the higher order method is an order of magnitude more efficient than the lower order method in modeling the flow for moderate-to-fine error tolerances. Accuracy, speed, and memory requirements are evaluated in the efficiency study.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.