Numerical simulations of three-dimensional flow over a multi-stage rocket using finite volumes

Abstract

The paper discusses the results obtained using an in-house developed finite volume code for three-dimensional, unstructured, adaptive meshes to simulate inviscid and viscous flows. A fully explicit, second-order accurate, five-stage, Runge–Kutta time-stepping scheme is used to perform the time march of the flow equations. Two different forms for flux calculation on the volume faces are implemented. The first one is a centered scheme which requires the addition of artificial dissipation terms. The other form for flux calculation is based on the van Leer flux-vector splitting scheme. The boundary conditions are set using Riemann invariants. The implementation uses a cell-centered, face-based data structure. The Spalart and Allmaras turbulence model is implemented to simulate viscous flows at high Reynolds numbers. In order to enhance the quality of the results, h-refinement routines are implemented in the code to adapt the original mesh. These routines are able to handle tetrahedra, hexahedra, triangular base prisms and quadrilateral base pyramids. A sensor based on density gradients selects the elements to be refined. The paper presents simulation results obtained for the Brazilian Satellite Launcher. The simulations using the adaptive mesh refinement routines are performed for inviscid flows. The paper also presents simulations of transonic and supersonic turbulent viscous flows over the vehicle.