Iterative method for the numerical solution of a system of integral equations for the heat conduction initial boundary value problem

11th International Conference on "Mesh methods for boundary-value problems and applications"

Svetushkov, N.N.^1

Applied Mathematics and Physics Department, Moscow Aviation Institute (National Research University), Volokolamskoe shosse 4, Moscow, Russia^1

关键词: Detonation waves;    Finding solutions;    Heat transfer process;    Initial-boundary value problems;    Iterative solutions;    Numerical algorithms;    Numerical solution;    System of integral equations;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/158/1/012091/pdf
DOI  :  10.1088/1757-899X/158/1/012091

来源: IOP

【 摘 要 】

The paper deals with a numerical algorithm to reduce the overall system of integral equations describing the heat transfer process at any geometrically complex area (both twodimensional and three-dimensional), to the iterative solution of a system of independent onedimensional integral equations. This approach has been called "string method" and has been used to solve a number of applications, including the problem of the detonation wave front for the calculation of heat loads in pulse detonation engines. In this approach "the strings" are a set of limited segments parallel to the coordinate axes, into which the whole solving area is divided (similar to the way the strings are arranged in a tennis racket). Unlike other grid methods where often for finding solutions, the values of the desired function in the region located around a specific central point here in each iteration step is determined by the solution throughout the length of the one-dimensional "string", which connects the two end points and set them values and determine the temperature distribution along all the strings in the first step of an iterative procedure.