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

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

Modeling of liquid fuel injection, evaporation and mixing in a gas turbine burner using large eddy simulations

The interaction of turbulence, temperature fluctuation, liquid fuel transport, mixing and evaporation is studied by using Large Eddy Simulations (LES). To assess the accuracy of the different components of the methods we consider first isothermal, single phase flow in a straight duct. The results using different numerical methods incorporating dynamic Sub-Grid-Scale (SGS) models are compared with DNS and experimental data. The effects of the interactions among turbulence, temperature fluctuation, spray transport, evaporation and mixing of the gaseous fuel are studied by using different assumptions on the temperature field. It has been found that there are strong non-linear interactions among temperature-fluctuation, evaporation and turbulent mixing which require additional modeling if not full LES is used. The developed models and methods have been applied to a gas turbine burner into which liquid fuel is injected. The dispersion of the droplets in the burner is described.</p