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A Scale-Residual Model for Large-Eddy Simulation
(1999)SAM Research ReportA subgrid-scale model for large-eddy simulation is developed and a conservative formulation of the filtered compressible Navier-Stokes equations is derived. We introduce a different way of looking at LES modelling: In contrast to other approaches, which estimate the subgrid-scale quantities explicitly out of the instantaneous filtered solution, the residual between the time evolution of two solutions of the Navier-Stokes equations (without ...Report -
The method of transport for nonlinear systems of hyperbolic conservation laws in several space dimensions
(1997)SAM Research ReportThe idea of the method of transport is introduced by means of non-linear conservation laws. The systems are rewritten in an advection form accounting for the characteristic propagation directions. A straightforward linearization of this advection form leads to a genuinely multi-dimensional method. Approximations using infinitely many or a finite number of propagation directions are shown.Report -
Multidimensional High Order Method of Transport for the Shallow Water Equations
(1996)SAM Research ReportThe Method of Transport was originally developed for the Euler equation in 1993 by M. Fey. He introduced the physical property of infinitely many propagation directions into the numerical method. Here, we present the extension of this method to equations with inhomogeneous fluxes, such as the shallow water equations. For efficiency reasons and to reach higher order accuracy certain modifications had to be made to the method, whereby the ...Report -
The Method of Transport for solving the Euler-equations
(1995)SAM Research ReportIn many technical applications it is necessary to compute a numerical solution of complex flow problems in several space dimensions. Most available codes split the multi-dimensional problem into several one-dimension\-al ones. Those are aligned with the cell interfaces of the underlying grid. In some of the applications, e.g.high Mach number flow, this approach does not work very well, since the physical properties of the model equations ...Report -
Decomposition of the multidimensional Euler equations into advection equations
(1995)SAM Research ReportBased on a genuine multi-dimensional numerical scheme, called Method of Transport, we derive a form of the compressible Euler-equations, capable of a linearization for any space dimension. This form allows a rigorous error analysis of the linearization error without the knowledge of the numerical method. The generated error can be eliminated by special correction terms in the linear equations. Hence, existing scalar high order methods can ...Report -
Multidimensional schemes for nonlinear systems of hyperbolic conservation laws
(1995)SAM Research ReportMost commonly used schemes for unsteady multidimensional systems of hyperbolic conservation laws use dimensional splitting. In each coordinate direction a scheme for a one dimensional system is used. Such an approach does not take in account the infinitely many propagation directions which are present in a system in several space dimensions. In 1992 M. Fey introduced what he called the Method of Transport, MoT, for the Euler equations of ...Report -
Multidimensional method of transport for the shallow water equations
(1995)SAM Research ReportA truly two-dimensional scheme based on a finite volume discretization on structured meshes will be developed for solving the shallow water equations. The idea of the method of transport, developed by M. Fey for the compressible Euler equations [6], is modified for our case. In contrast to this, the flux of the shallow water equations is not homogeneous. Hence, the eigenvectors of the Jacobi matrix of the flux can not be used to decompose ...Report -
Stagnation point analysis
(1992)SAM Research ReportThe numerical solution of a symmetric hypersonic blunt body flow in two space dimensions is considered, and the problem of the arising chemical boundary layer is discussed. Analytical and numerical investigations are used to analyze the solution on the stagnation point streamline. We point out the necessary assumptions to obtain an equivalent system of ordinary differential equations along this line and to get a unique solution. We also ...Report -
The influence of a source term, an example: chemically reacting hypersonic flow
(1992)SAM Research ReportWe show, by way of an example, that the solution of a system of hyperbolic conservation laws exhibits an unexpected behavior if a source term is present. The example is the system of Euler equations for N species in two space dimensions. If the source term is not present and in the initial and inflow conditions a fixed mixture of species is prescribed then the solution basically behaves like the flow of an ideal gas, except that there are ...Report -
Special aspects of reacting inviscid blunt body flow
(1992)SAM Research ReportThe problem of a hypersonic blunt body flow in two space dimensions is considered. The governing inhomogeneous Euler equations are given and the special treatment of calorically non-perfect gas in chemical non-equilibrium is described. The chemical model is given. The problem of the arising chemical boundary layer is discussed. Analytical and numerical investigations are used to analyse this boundary layer and to get error estimates for ...Report