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Liu, D. (2004) Spectral Element/Force Coupling Method: Application to Colloidal Micro-Devices and Self-Assembled Particles Structures in 3D Domains. Ph.D. Dissertation, Brown University, Providence.

has been cited by the following article:

• TITLE: Spectral Element Simulation of Rotating Particle in Viscous Flow

  AUTHORS: Don Liu, Ning Zhang

  KEYWORDS: Spectral Element Method, High Order Method, Orthogonal Polynomials, Particle Fluid Intereaction, Navier-Stokes Equations, Translation and Rotation

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.4 No.7, July 25, 2016

  ABSTRACT: Spectral element methods (SEM) are superior to general finite element methods (FEM) in achieving high order accuracy through p-type refinement. Owing to orthogonal polynomials in both expansion and test functions, the discretization errors in SEM could be reduced exponentially to machine zero so that the spectral convergence rate can be achieved. Inherited the advantage of FEM, SEM can enhance resolution via both h-type and p-type mesh-refinement. A penalty method was utilized to compute force fields in particulate flows involving freely moving rigid particles. Results were analyzed and comparisons were made; therefore, this penalty-implemented SEM was proven to be a viable method for two-phase flow problems.