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A novel spatial-temporal collocation solver for long-time transient diffusion with time-varying source terms
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DOI：10.1016/j.enganabound.2024.106060.png)
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Abstract
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In this paper, a novel spatial-temporal collocation solver is proposed for the solution of 2D and 3D long-time diffusion problems with source terms varying over time. In the present collocation solver, a series of semianalytical spatial-temporal fundamental solutions are used to approximate the solutions of the time-dependent diffusion equations with only the node discretization of the initial and boundary conditions. This approach avoids the numerical inverse Laplace/Fourier transformations or the selection of the time-step size in the traditional time discretization methods (Laplace/Fourier transformations and time-stepping scheme, etc.). To treat with the time-varying source terms, an extension of the multiple reciprocity method from the spatial domain to the spatial-temporal domain is achieved, which converts the nonhomogeneous governing equation into a high-order partial differential equation via a series of differential operators without the need for additional discretization in the spatial-temporal domain. Several numerical examples validate the feasibility, efficiency and accuracy of the proposed solver.
Keywords:
Diffusion
Semi-analytical
Spatial-temporal
Fundamental solution
Multiple reciprocity
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