Advanced Implicit Meshless Approaches for the Rayleigh–Stokes Problem for a Heated Generalized Second Grade Fluid with Fractional Derivative

Author:

Bi Xiaolei1,Mu Shanjun1,Liu Qingxia2ORCID,Liu Quanzhen1,Liu Baoquan1,Zhuang Pinghui2,Gao Jian1,Jiang Hui1,Li Xin3,Li Bochen3

Affiliation:

1. SINOPEC Research Institute of Safety Engineering, Qingdao 266071, Shandong, P. R. China

2. School of Mathematical Sciences, Xiamen University, Xiamen 361005, Fujian, P. R. China

3. Xiamen Taihang Technology Co., Ltd, Xiamen 361000, Fujian, P. R. China

Abstract

To solve the Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivative in a bounded domain is important in the research for diffusion processes. In this paper, novel implicit meshless approaches based on the moving least squares (MLS) approximation for spatial discretization and two different time discrete schemes, which are the first-order semi-discrete scheme and the second-order semi-discrete scheme for time, are developed for the numerical simulation of the Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivative in a bounded domain. Based on these two time discretization schemes, the newly developed meshless approaches will have the first-order and the second-order accuracy in time, respectively. The stability and convergence of the implicit MLS meshless approaches are discussed and theoretically proven. Numerical examples with different problem domains and different nodal distributions are studied to validate and investigate accuracy and efficiency of the newly developed meshless approaches. It has found that the newly developed meshless approaches are accurate and convergent for fractional partial differential equations (FPDEs). Most importantly, the meshless approaches are robust for arbitrarily distributed nodes and complex domains.

Funder

The Fundamental Research Funds for the Central Universities

Open Issues of State Key Laboratory of Chemical Safety

Publisher

World Scientific Pub Co Pte Lt

Subject

Computational Mathematics,Computer Science (miscellaneous)

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