Journal of Advances in Mathematics and Computer Science

This work focuses on a numerical simulation of reentry 3D-flows using high order resolution schemes. Euler and Navier-Stokes equations are studied, on conservative and finite volume approaches, and employing structured spatial discretization. The ENO (Essentially Non-Oscillatory) procedure is presented to a conserved variable interpolation process, using either the Newton method, to second-, third-, fourth- and fifth-orders of accuracy, or the Hermite method, to third- and fifth-orders of accuracy. Furthermore, the WENO (Weighted Essentially Non-Oscillatory) procedure is also tested, using the Newton interpolation process, to generate third- and fifth-orders of accuracy solutions. Results applying the MUSCL scheme (Monotone Upstream-centered Schemes for Conservation Laws) are also presented and serve as TVD (Total Variation Diminishing) benchmark purpose. In this context, the “hot gas” hypersonic thermochemical non-equilibrium 3D-flow around a blunt body has been simulated. The convergence process is accelerated to steady-state condition through a spatially variable time step procedure, which has proved effective gains in terms of computational acceleration. The reactive simulations involve Earth atmosphere chemical models of five and seven species, based on the Saxena and Nair and Blottner models, respectively. Results showed that the ENO procedure using Newton 5th-order interpolation scheme presents better overall solutions.