Computer Simulation System of Nonlinear Thermal Conductivity

Abstract

The article discusses the computer simulation system of nonlinear processes that described by the one-dimensional nonstationary heat equation with power-law nonlinearity. The solution of the nonlinear heat equation is realized by meshless scheme, which is based on combination of the collocation method and radial basis functions. Radial basis functions are used to approximate the solution of a partial differential equation, while the collocation method is used to determine unknown coefficients. The computer simulation system allows is used the following radial basis functions: Gaussian, multiquadric, inverse quadratic, and inverse multiquadric. The computer simulation system allows setting the initial and boundary conditions of the boundary-value problem. In the computer simulation system, it is possible to set such parameters of the solution as the exponent in the nonlinear heat equation, the coefficient of thermal conductivity, the density, the specific heat at constant pressure, the size of the domain of the boundary-value problem, the distance between interpolation nodes, the time interval of the nonstationary boundary-value problem, the time step, and the shape parameter of the radial basis function. The visualization of an approximate solution of the one-dimensional nonstationary heat equation with power-law nonlinearity is realized in the form of the three-dimensional surface in the computer simulation system. The computer simulation system allows visualization of the solution at chosen time steps as three-dimensional plots. The results of numerical calculations are demonstrated by the benchmark problem that simulates the stopping of a heat wave front in a heat equation with power-law nonlinearity.