Unsteady aerodynamic calculations using three-dimensional Euler equations on unstructured dynamic grids

Abstract This paper presents an algorithm to solve the three-dimensional unsteady Euler equations on unstructured tetrahedral meshes using a dynamic mesh algorithm. The driving algorithm is an upwind biased implicit second order accurate cell-centered finite volume scheme. The spatial discretisation technique involves a naturally dissipative flux-split approach that accounts for the local wave propagation characteristics of the flow and captures shock waves sharply. A continuously differentiable flux limiter has been employed to eliminate the spurious oscillations near shock waves, generally arising in calculations involving upwind biased schemes. The temporal discretisation is also second order accurate and uses a Newton linearisation for unsteady calculations. To calculate time dependent flows a dynamic mesh algorithm has been implemented in which the mesh is moved to conform to the instantaneous position of the body by modelling each edge of each cell by a spring. The paper presents a description of the solver and the grid movement algorithm along with results and comparison that assess their capabilities.