Derivation of a spectral pressureless formulation for direct numerical simulation of incompressible channel flows based on a functional formalism

• Published in: Journal of non-Newtonian fluid mechanics Vol. 120; no. 1; pp. 241 - 250
• Main Authors: Edwards, Brian J, Beris, Antony N
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Amsterdam Elsevier B.V 01.07.2004; Elsevier
• Subjects: Computational methods in fluid dynamics; Direct numerical simulation; Divergence-free flow; Exact sciences and technology; Flows in ducts, channels, nozzles, and conduits; Fluid dynamics; Fundamental areas of phenomenology (including applications); Non-newtonian fluid flows; Nonequilibrium and irreversible thermodynamics; Physics; Spectral methods; Statistical physics, thermodynamics, and nonlinear dynamical systems; Thermodynamics; Turbulent channel flow; Turbulent channel flow; Direct numerical simulation; Spectral methods; Divergence-free flow; Thermodynamics; Spectral method; Algorithms; Turbulent flow; Pipe flow; Three dimensional flow; Non equilibrium system; Digital simulation; Incompressible fluid; Non-Newtonian fluids
• ISSN: 0377-0257; 1873-2631
• DOI: 10.1016/j.jnnfm.2004.02.010

In this article, a new computational spectral algorithm is developed for simulation of general three-dimensional, time-dependent, incompressible channel flow. The development is based on a general functional formalism of non-equilibrium thermodynamics, and, although it is illustrated here for a Newtonian fluid, it is easily adapted to non-Newtonian fluids. The advantage of this algorithm is that the scalar pressure is eliminated from the discrete spectral analog to the equations of motion, which are expressed solely in terms of the spectral coefficients of the velocity vector field. This alleviates the need for the application of boundary conditions on the pressure, the specification of which can be a major source of difficulty in direct numerical simulations. At the same time, the velocity spectrum is quite general, and not subject to any a priori constraints. Thus, it is anticipated that the ideas exposed in the present algorithm can lead to the development of better numerical simulation techniques for complicated three-dimensional and turbulent flows.