Some aspects of algorithm performance and modeling in transient analysis of structures

The status of an effort to increase the efficiency of calculating transient temperature fields in complex aerospace vehicle structures is described. The advantages and disadvantages of explicit algorithms with variable time steps, known as the GEAR package, is described. Four test problems, used for evaluating and comparing various algorithms, were selected and finite-element models of the configurations are described. These problems include a space shuttle frame component, an insulated cylinder, a metallic panel for a thermal protection system, and a model of the wing of the space shuttle orbiter. Results generally indicate a preference for implicit over explicit algorithms for solution of transient structural heat transfer problems when the governing equations are stiff (typical of many practical problems such as insulated metal structures)

The use of the mesh free methods (radial basis functions) in the modeling of radionuclide migration and moving boundary value problems

Recently, the mesh free methods (radial basis functions-RBFs) have emerged as a novel computing method in the scientific and engineering computing community. The numerical solution of partial differential equations (PDEs) has been usually obtained by finite difference methods (FDM), finite element methods (FEM) and boundary elements methods (BEM). These conventional numerical methods still have some drawbacks. For example, the construction of the mesh in two or more dimensions is a nontrivial problem. Solving PDEs using radial basis function (RBF) collocations is an attractive alternative to these traditional methods because no tedious mesh generation is required. We compare the mesh free method, which uses radial basis functions, with the traditional finite difference scheme and analytical solutions. We will present some examples of using RBFs in geostatistical analysis of radionuclide migration modeling. The advection-dispersion equation will be used in the Eulerian and Lagrangian forms. Stefan's or moving boundary value problems will also be presented. The position of the moving boundary will be simulated by the moving data centers method and level set method

The Laplace transform boundary element method for diffusion-type problems

Diffusion-type problems are described by parabolic partial differential equations; they are defined on a domain involving both time and space. The usual method of solution is to use a finite difference time-stepping process which leads to an elliptic equation in the space variable. The major drawback with the finite difference method in time is the possibility of severe stability restrictions. An alternative process is to use the Laplace transform. The transformed problem can be solved using a suitable partial differential equation solver and the solution is transformed back into the time domain using a suitable inversion process. In all practical situations a numerical inversion is required. For problems with discontinuous or periodic boundary conditions, the numerical inversion is not straightforward and we show how to overcome these difficulties. The boundary element method is a well-established technique for solving elliptic problems. One of the procedures required is the evaluation of singular integrals which arise in the solution process and a new formulation is developed to handle these integrals. For the solution of non-homogeneous equations an additional technique is required and the dual reciprocity method used in conjunction with the boundary element method provides a way forward. The Laplace transform is a linear operator and as such cannot handle non-linear terms. We address this problem by a linearisation process together with a suitable iterative scheme. We apply such a procedure to a non-linear coupled electromagnetic heating problem with electrical and thermal properties exhibiting temperature dependencies