A Numerical Investigation of Blow-up in The Moving Heat Source Problems in Two-dimensions
نویسندگان
چکیده
The temperature of a combustible material will rise or even blow up when a heat source moves across it. In this paper, we study the blow-up phenomenon in this kind of moving heat source problems in two-dimensions. First, a two-dimensional heat equation with a nonlinear source term is introduced to model the problem. The nonlinear source is localized around a circle which is allowed to move. By using the coordinate transformation, the equation is simplified to a one-dimensional one. Then it is solved by the moving collocation method. The numerical results show that the blow-up occurs if the speed of the heat source is slow, and the blow-up is avoided when the heat source moves fast enough. Key–Words: Moving heat source, Blow-up, Moving mesh method, Reaction-diffusion equation, Moving collocation method, Local absorbing boundary conditions
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