COMPUTER SIMULATION OF TWO-DIMENSIONAL NONSTATIONARY HEAT CONDUCTION PROBLEMS BY MESHLESS APPROACH USING ATOMIC RADIAL BASIS FUNCTIONS
Keywords:
meshless approach, atomic radial basis functions, dual reciprocity method, method of fundamental solutions, boundary-value problems, nonstationary heat conduction problems, computer simulation systemAbstract
This article is devoted to the development and implementation of the computer simulation system "MHT2D" is designed to solve numerically two-dimensional nonstationary heat conduction problems by meshless approach using atomic radial basis functions of two independent variables. Solution of the boundary-value problem of heat conduction in the computer simulation system "MHT2D" is based on the combination of the dual reciprocity method and the method of fundamental solutions using atomic radial basis functions. To avoid integration over a domain, the method of partial solutions is used, which divides the solution of an inhomogeneous equation into a partial and a homogeneous ones. The method of fundamental solutions is used to obtain homogeneous solution and the dual reciprocity method with atomic radial basis functions is used to obtain particular solution. As a result, such approach implements the completely meshless method. The input data for the computer simulation system is the PLT file, which contains information about the geometric domain of the boundary-value problem. In the computer simulation system "MHT2D", the following radial basis functions are available: Gaussian, multiquadratic, inverse quadratic and inverse multiquadratic. The computer simulation system "MHT2D" it is possible to set values of initial and boundary conditions. Also, the computer simulation system "MHT2D" it is possible to set value of the internal heat source, thermal conductivity, density and specific heat at constant pressure. In the computer simulation system "MHT2D" it is possible to set the number of interpolation nodes, the number of nodes on the boundary, the time interval, the time step, and the number of nodes on the fictitious boundary. The computer simulation system "MHT2D" performs visualization of the solution of boundary-value problem in form of surface, which is the distribution of the temperature field at the current time. In the computer simulation system "MHT2D" realized an animated visualization of the temperature field distribution on the given time interval for nonstationary boundary-value problems.
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