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Meshless and analytical solutions to the time-dependent advection-diffusion-reaction equation with variable coefficients and boundary conditions

机译:变系数和边界条件的时变对流扩散反应方程的无网格和解析解

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摘要

A variety of physical problems in science may be expressed using the advection-diffusion-reaction (ADR) equation that covers heat transfer and transport of mass and chemicals into a porous or a nonporous media. In this paper, the meshless generalised reproducing kernel particle method (RKPM) is utilised to numerically solve the time-dependent ADR problem in a general n-dimensional space with variable coefficients and boundary conditions. A time-dependent Robin boundary condition is formulated and precisely enforced in a novel approach. The accuracy and robustness of the meshless solution is verified against finite element simulations and a general one-dimensional analytical solution obtained in this study.
机译:对流扩散反应(ADR)方程可以表示科学中的各种物理问题,该方程涵盖了物质和化学物质向多孔介质或无孔介质的热传递和传递。本文采用无网格广义再生核粒子法(RKPM),以数值方法求解了具有可变系数和边界条件的一般n维空间中与时间有关的ADR问题。提出了一种时变的Robin边界条件,并用一种​​新颖的方法精确地执行了该条件。通过有限元模拟和本研究获得的通用一维解析解,验证了无网格解的准确性和鲁棒性。

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