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The numerical solution of stefan problems with front-tracking and smoothing methods
Mean-square stability analysis of approximations of stochastic differential equations in infinite dimensions
The (asymptotic) behaviour of the second moment of solutions to stochastic
differential equations is treated in mean-square stability analysis. This
property is discussed for approximations of infinite-dimensional stochastic
differential equations and necessary and sufficient conditions ensuring
mean-square stability are given. They are applied to typical discretization
schemes such as combinations of spectral Galerkin, finite element,
Euler-Maruyama, Milstein, Crank-Nicolson, and forward and backward Euler
methods. Furthermore, results on the relation to stability properties of
corresponding analytical solutions are provided. Simulations of the stochastic
heat equation illustrate the theory.Comment: 22 pages, 4 figures; deleted a section; shortened the presentation of
results; corrected typo
Base recirculation flow prediction using a time-dependent finite-difference technique Final report
Numerical determination of three dimensional base recirculation gas flow from multiple clustered nozzle
Computation of three-dimensional nozzle-exhaust flow fields with the GIM code
A methodology is introduced for constructing numerical analogs of the partial differential equations of continuum mechanics. A general formulation is provided which permits classical finite element and many of the finite difference methods to be derived directly. The approach, termed the General Interpolants Method (GIM), can combined the best features of finite element and finite difference methods. A quasi-variational procedure is used to formulate the element equations, to introduce boundary conditions into the method and to provide a natural assembly sequence. A derivation is given in terms of general interpolation functions from this procedure. Example computations for transonic and supersonic flows in two and three dimensions are given to illustrate the utility of GIM. A three-dimensional nozzle-exhaust flow field is solved including interaction with the freestream and a coupled treatment of the shear layer. Potential applications of the GIM code to a variety of computational fluid dynamics problems is then discussed in terms of existing capability or by extension of the methodology
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