Wenzhi Xu , Zhuojia Fu , Qiang Xi , Qingguo Liu , Božidar Šarler
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A novel spatial-temporal collocation solver for long-time transient diffusion with time-varying source terms
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 semi-analytical 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.
期刊介绍:
This journal is specifically dedicated to the dissemination of the latest developments of new engineering analysis techniques using boundary elements and other mesh reduction methods.
Boundary element (BEM) and mesh reduction methods (MRM) are very active areas of research with the techniques being applied to solve increasingly complex problems. The journal stresses the importance of these applications as well as their computational aspects, reliability and robustness.
The main criteria for publication will be the originality of the work being reported, its potential usefulness and applications of the methods to new fields.
In addition to regular issues, the journal publishes a series of special issues dealing with specific areas of current research.
The journal has, for many years, provided a channel of communication between academics and industrial researchers working in mesh reduction methods
Fields Covered:
• Boundary Element Methods (BEM)
• Mesh Reduction Methods (MRM)
• Meshless Methods
• Integral Equations
• Applications of BEM/MRM in Engineering
• Numerical Methods related to BEM/MRM
• Computational Techniques
• Combination of Different Methods
• Advanced Formulations.