Runge-Kutta residual distribution schemes

We are concerned with the solution of time-dependent non-linear hyperbolic partial differential equations. We investigate the combination of residual distribution methods with a consistent mass matrix (discretisation in space) and a Runge–Kutta-type time-stepping (discretisation in time). The introduced non-linear blending procedure allows us to retain the explicit character of the time-stepping procedure. The resulting methods are second order accurate provided that both spatial and temporal approximations are. The proposed approach results in a global linear system that has to be solved at each time-step. An efficient way of solving this system is also proposed. To test and validate this new framework, we perform extensive numerical experiments on a wide variety of classical problems. An extensive numerical comparison of our approach with other multi-stage residual distribution schemes is also given

Compact third-order multidimensional upwind discretization for steady and unsteady flow simulations

We propose a new third-order multidimensional upwind algorithm for the solution of the flow equations on tetrahedral cells unstructured grids. This algorithm has a compact stencil (cell-based computations) and uses a finite element idea when computing the residual over the cell to achieve its third-order (spatial) accuracy. The construction of the new scheme is presented. The asymptotic accuracy for steady or unsteady, inviscid or viscous flow situations is proved using numerical experiments. The new high-order discretization proves to have excellent parallel scalability. Our studies show the advantages of the new compact third-order scheme when compared with the classical second-order multidimensional upwind schemes

LES of spray in compressible flows on unstructured grids

In this paper we report some results of our numerical simulations of sprays in compressible flows using Large Eddy Simulation. The combined LES- and spray code has been applied to the computation of the flow and spray injection into a swirl generator of a gas-turbine. The interaction between the spray jet and the flow field has been investigated. A dynamic SGS model has been used and results have been compared with the experimental data

Large eddy simulation of shock boundary layer interaction in a transonic internal flow

The paper presents a study of the dynamics of non-stationary shock wave and its interaction with the boundary layer in a transonic flow inside a channel with a bump. The turbulent flow is handled using Large Eddy Simulations (LES). The computations are done with the recently developed multidimensional upwind scheme and with two other commercial codes. The aim is to improve the understanding of the mechanism of shock wave dynamics, viscous/inviscid and the presence of solution hysteresis. The numerical results are compared to available experimental data

Study of mixing in swirling turbulent jets

Large Eddy Simulation of swirling flows in a typical gas turbine burner has been carried out. The goal has been to study the effects of swirl number, inlet velocity profile, confining wall distance, Reynolds- and Schmidt-number effects on the flow and turbulent mixing. The results show that the inlet velocity profile, the confinement and the swirl have a substantial effect on the resulting flow-field, while the values of the Reynolds- and Schmidt-numbers are of less importance in our case