Stochastic finite difference lattice Boltzmann method for steady incompressible viscous flows

Journal Article · Fri Aug 20 00:00:00 EDT 2010 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2010.04.041· OSTI ID:21417238

So, R M.C. ^[1]; Leung, W W.F. ^[2]

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1. Building Services Engineering Department, Hong Kong Polytechnic University, Hung Hom (Hong Kong)
2. Research Institute of Innovative Products and Technologies, Hong Kong Polytechnic University, Hung Hom (Hong Kong)

With the advent of state-of-the-art computers and their rapid availability, the time is ripe for the development of efficient uncertainty quantification (UQ) methods to reduce the complexity of numerical models used to simulate complicated systems with incomplete knowledge and data. The spectral stochastic finite element method (SSFEM) which is one of the widely used UQ methods, regards uncertainty as generating a new dimension and the solution as dependent on this dimension. A convergent expansion along the new dimension is then sought in terms of the polynomial chaos system, and the coefficients in this representation are determined through a Galerkin approach. This approach provides an accurate representation even when only a small number of terms are used in the spectral expansion; consequently, saving in computational resource can be realized compared to the Monte Carlo (MC) scheme. Recent development of a finite difference lattice Boltzmann method (FDLBM) that provides a convenient algorithm for setting the boundary condition allows the flow of Newtonian and non-Newtonian fluids, with and without external body forces to be simulated with ease. Also, the inherent compressibility effect in the conventional lattice Boltzmann method, which might produce significant errors in some incompressible flow simulations, is eliminated. As such, the FDLBM together with an efficient UQ method can be used to treat incompressible flows with built in uncertainty, such as blood flow in stenosed arteries. The objective of this paper is to develop a stochastic numerical solver for steady incompressible viscous flows by combining the FDLBM with a SSFEM. Validation against MC solutions of channel/Couette, driven cavity, and sudden expansion flows are carried out.

• OSTI ID: 21417238
• Journal Information: Journal of Computational Physics, Vol. 229, Issue 17; Other Information: DOI: 10.1016/j.jcp.2010.04.041; PII: S0021-9991(10)00228-7; Copyright (c) 2010 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
ALGORITHMS
ARTERIES
BLOOD FLOW
BOUNDARY CONDITIONS
CHAOS THEORY
COMPRESSIBILITY
COMPUTERIZED SIMULATION
FINITE ELEMENT METHOD
INCOMPRESSIBLE FLOW
MONTE CARLO METHOD
NAVIER-STOKES EQUATIONS
POLYNOMIALS
STOCHASTIC PROCESSES
VALIDATION
VISCOUS FLOW
BLOOD VESSELS
BODY
CALCULATION METHODS
CARDIOVASCULAR SYSTEM
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUID FLOW
FUNCTIONS
MATHEMATICAL LOGIC
MATHEMATICAL SOLUTIONS
MATHEMATICS
MECHANICAL PROPERTIES
NUMERICAL SOLUTION
ORGANS
PARTIAL DIFFERENTIAL EQUATIONS
SIMULATION
TESTING