Solutions In Complex Domains Research Articles

A Review of Mathematical Models of Elasticity Theory Based on the Methods of Iterative Factorizations and Fictitious Components

This review analyzes articles on mathematical modeling of elasticity theory using iterative factorizations and fictitious components. To carry out this study, various methods are developed, for example, an approximate analytical method of iterative factorizations for calculating the displacements of a rectangular plate, and a modified method of fictitious components for calculating the continuous displacement of plates. The performed calculations confirm the effectiveness of these methods. Descriptions of solutions to problems of elasticity theory and possible applications of the considered mathematical models and methods are given. An overview of the methods used to solve these problems is given. Particular attention is paid to problematic issues that arise in solving these problems. Techniques used to reduce complex problems to the solution of simple problems are given, for example, the lowering of the order of differential equations and the reduction of solutions in complex domains to solutions in a simple domain. For the first approach, iterative factorization methods are often used, and for the second, methods of the fictitious component type are often used. The main presentation in this review is focused on the approximate solution of elliptic boundary value problems. The works considered in the review raise questions about the development of methods in research on fictitious domains, fictitious components, and iterative factorizations.

Numerical treatment of mass continuity in pressure-correction methods for patient specific flow simulations

PurposeThe purpose of this paper is the development of a robust numerical scheme for fluid flow simulations in complex domains with open boundaries.Design/methodology/approachA modified pressure correction algorithm is presented. The proposed modifications are derived through a step-by-step analysis of the importance of mass continuity enforcement in pressure correction methods, the boundary conditions of the pressure correction equation and the special nature of open boundaries.FindingsThe algorithm is validated by performing steady state laminar flow simulations in two backward facing step geometries with progressively truncated outlet channels. The efficiency of the methodology is demonstrated by simulating the pulsatile flow field in a patient specific iliac bifurcation reconstructed by medical imaging data.Originality/valueThe proposed numerical scheme provides accurate and mass conserving solutions in complex domains with open boundaries. The proposed methodology may be directly implemented in any computational domain without any prerequisites regarding the location or type of domain boundaries.

Large-Eddy Simulation of a Wing Tip Vortex on Overset Grids

A multiblock large-eddy simulation (LES) code with overset grid capability is reported on that has been developed primarily to study the tip vortex noise problem arising on rotating wind-turbine blades. The LES code can also be used to simulate the tip vortices around nonrotating wing geometries typically found in aeronautical applications. It employs state-of-the-art compact finite differencing, implicit spatial filtering, and nonreflecting boundary conditions on free boundaries, as well as characteristic-type boundary conditions on solid walls. High-order-accurate interpolation is used for the transfer of information among the individual component grids that make up the overset grid topology. The multiblock nature and the overset grid capability of the code allow high-order accurate numerical solutions in complex domains. Results for the tip vortex around a nonrotating wing with a rounded tip are presented to demonstrate the capability of the code. Comparisons of the numerical results with experimental data are also carried out.

HIGH-ORDER ACCURATE NUMERICAL SCHEMES FOR THE PARABOLIC EQUATION

Efficient, high-order accurate methods for the numerical solution of the standard (narrow-angle) parabolic equation for underwater sound propagation are developed. Explicit and implicit numerical schemes, which are second- or higher-order accurate in time-like marching and fourth-order accurate in the space-like direction are presented. The explicit schemes have severe stability limitations and some of the proposed high-order accurate implicit methods were found conditionally stable. The efficiency and accuracy of various numerical methods are evaluated for Cartesian-type meshes. The standard parabolic equation is transformed to body fitted curvilinear coordinates. An unconditionally stable, implicit finite-difference scheme is used for numerical solutions in complex domains with deformed meshes. Simple boundary conditions are used and the accuracy of the numerical solutions is evaluated by comparing with an exact solution. Numerical solutions in complex domains obtained with a finite element method show excellent agreement with results obtained with the proposed finite difference methods.

Three Dimensional Numerical Analysis of Screw Compressor Performance

Modern manufacturing methods enable screw compressors to be constructed to very close tolerances where full 3-D numerical calculation of the heat and fluid flow through them is then required to obtain the maximum possible improvements in their design. An independent stand-alone interface program has been developed by the authors in order to generate a numerical grid for this purpose. The interface employs a procedure to produce rotor profiles and an analytical transfinite interpolation method with adaptive meshing to obtain a fully structured 3-D numerical mesh, which is directly transferable to a CFD code. This was required to overcome problems associated with moving, stretching and sliding rotor domains and with robust calculations in domains with significantly different geometry ranges. Some changes had to be made within the solver functions both to enable calculations and to make them faster. These include a means to maintain constant pressures at the inlet and outlet ports and consideration of two-phase flow resulting from oil injection in the working chamber. Modifications implemented to the CFD procedure improved solutions in complex domains with strong pressure gradients. The pre-processor code and calculating method have been tested on a commercial CFD solver to obtain flow simulations and integral parameter calculations. The results of calculations on an oil injected screw compressor are presented in this paper and compared with experimental results.