Two-Level Finite Element Approximation for Oseen Viscoelastic Fluid Flow

Mathematics

Shahid Hussain¹  NasrinJahan Nasu¹  Md.Abdullah Al Mahbub¹  Haibiao Zheng¹ 

[1] School of Mathematical Sciences, East China Normal University, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, Shanghai 200241, China;

关键词: viscoelastic fluid flow;    two-level method;    DG method;    Oseen viscoelastic fluid flow model;   

DOI  :  10.3390/math6050071

来源: DOAJ

【 摘 要 】

In this paper, a two-level finite element method for Oseen viscoelastic fluid flow obeying an Oldroyd-B type constitutive law is presented. With the newly proposed algorithm, solving a large system of the constitutive equations will not be much more complex than the solution of one linearized equation. The viscoelastic fluid flow constitutive equation consists of nonlinear terms, which are linearized by taking a known velocityb ( x ), and transforms into the Oseen viscoelastic fluid flow model. Since Oseen viscoelastic fluid flow is already linear, we use a two-level method with a new technique. The two-level approach is consistent and efficient to study the coupled system which contains nonlinear terms. In the first step, the solution on the coarse grid is derived, and the result is used to determine the solution on the fine mesh in the second step. The decoupling algorithm takes two steps to solve a linear system on the fine mesh. The stability of the algorithm is derived for the temporal discretization and obtains the desired error bound. Two numerical experiments are executed to show the accuracy of the theoretical analysis. The approximations of the stress tensor, velocity vector, and pressure field areP 1-discontinuous,P 2-continuous andP 1-continuous finite elements respectively.

【 授权许可】

Unknown