Complex Boundary Element Method Research Articles

Numerical Simulation of the Nonstationary Process of the Shot Based on the Navier – Stokes Equations

This paper gives a spatial mathematical formulation of the problem of internal ballistics based on the Navier – Stokes equations, taking into account the swirl of the flow due to the rotation of the projectile. The k-e model of turbulent viscosity is used. The control volume method is used for the numerical solution of systems of equations. The gas parameters at the boundaries of the control volumes are determined by the method of S. K. Godunov using a self-similar solution to the problem of the decay of an arbitrary discontinuity. The MUSCL scheme is used to increase the order of approximation of the difference method. For equations written in a cylindrical coordinate system, an orthogonal difference grid is constructed using the complex boundary element method. A comparative analysis of the results obtained with different approaches to modeling the process of an artillery shot is given. Quantitative data are presented on the influence of factors not previously taken into account on the characteristics of the process.

Solution of Large Complex BEM Systems Derived From High-Resolution Human Models

The aim of this paper is the investigation of the numerical properties of the boundary element method (BEM) when applied to dosimetric analysis of human exposure to electromagnetic fields adopting high resolution voxel-based data sets. Some test problems are analyzed considering the neck region of the human body radiated by a loop antenna. Different strategies in the development of the problem equations are proposed and their effects on the conditioning of the BEM matrix are discussed. Several direct and iterative solvers are applied to the model problems and their efficiency is compared.

The study of the potential flow past a submerged hydrofoil by the complex boundary element method

Abstract We study the free-boundary linearized problem of the two-dimensional steady potential flow past a submerged hydrofoil. The integral representation obtained herein for the complex velocity involves only finite contours. The corresponding integral equation may be solved for any streamlined hydrofoil by means of the complex boundary element method. We calculate the free surface elevation, the velocity field, the pressure coefficients, the lift and the drag for the Karman–Trefftz and Joukowsky hydrofoils and for the circular obstacle. A comparison between some numerical and analytical results shows a very good agreement.

Motion of a vertical wall fixed on springs under the action of surface waves

A two-dimensional unsteady hydroelastic problem of interaction between surface waves and a moving vertical wall fixed on springs is studied. An analytical solution of the problem is constructed using a linear approximation, and a numerical solution within the framework of a nonlinear model of a potential fluid flow is found by a complex boundary element method. By means of analysis of the linear and nonlinear solutions, it is found that the linear solution can be used to predict some important characteristics of the wall motion and the fluid flow in the case of moderate wave amplitudes.

The Riemann complex boundary element method for the solutions of two-dimensional Elliptic equations

In this paper, a new boundary integral equation model Riemann complex boundary element method (RCBEM), is proposed based on the boundary element method (BEM) and the theory of Vekua and its modification as well as complex Riemann function as the fundamental solution. The RCBEM method is used to solve the linear, second order, elliptical partial differential equations in the fluid flow problems. In comparison to the generally used BEM, for RCBEM, there are two distinct differences. First one is that, RCBEM applies complex Riemann function as the fundamental solution of the adjoint operator while in direct BEM, on the other hand Green function is used. The second one is that the governing equations should be transformed into complex domain because there exist two characteristics in complex plane for elliptic systems, while in the direct BEM is not, since the Green function is adopted instead. The singular problem occurring in direct BEM can be avoided in RCBEM, especially for regular domain problems. The efficiency and accuracy of the RCBEM depends on the complex variable integration. To verify the feasibility and accuracy of RCBEM, the model is applied to different case studies of potential flows, Helmholtz equation problem and advection–diffusion problem and results are compared with analytical solutions and other numerical models. The results are satisfactory and prove the applicability of RCBEM for various two-dimensional elliptic equation problems.

Extension of the CVBEM to higher-order trial functions

The higher-order trial functions, such as the parabolic, cubic, and Hermite cubic polynomial functions, for the complex boundary element method are derived and their computer programs are developed. Using the considered higher-order trial function, models obtained compatible results to the linear trial function model.