A Projection-Based Variational Multiscale Method for Large-Eddy Simulation With Application to Non-Isothermal Free Convection Problems

Abstract

We consider a projection-based variational multiscale method for large-eddy simulation of the Navier–Stokes/Fourier model of incompressible, non-isothermal flows. For the semidiscrete problem, an a priori error estimate is given for rather general nonlinear, piecewise constant coefficients of the subgrid models for the unresolved scales of velocity, pressure, and temperature. Then we address aspects of the discretization in time. Finally, the design of the subgrid scale models is specified for the case of free convection problems and studied for the standard benchmark problem of free convection in a closed cavity.

A Review of Variational Multiscale Methods for the Simulation of Turbulent Incompressible Flows

“…In (109), {τ c } K∈T h is a family of stabilization parameters which are usually defined to be piecewise constant. Using this proposal, the small resolved pressure does not appear any longer in the large scale equation but its influence on the large scales is modeled.…”

“…Note that both models for the small resolved scale (109) and (112) can be interpreted in the way that the small resolved scales are driven from the residual of the large scales. The small resolved pressure is driven from the residual of the continuity equation and the small resolved velocity from the residual of the momentum equation.…”

“…Finally, the results of [94] were generalized in [123] to the case of ν T being a piecewise constant viscosity. The analysis from [123] was extended in [109] to the case of thermally coupled incompressible flows.…”

Local projection FEM stabilization for the time‐dependent incompressible Navier–Stokes problem

“…In this article, we consider stabilized finite element (FE) approximations of problem (1)- (4). In particular, inf-sup stable velocity-pressure FE pairs are chosen together with local projection stabilization (LPS).…”

A projection-based stabilized finite element method for steady-state natural convection problem

“…In the meantime, some numerical analysis and numerical results for the time-dependent natural convection equation can be found in literature [19,2]. To do authors best knowledge, the error estimates of the projection-based stabilization is applied to steady-state natural convection equations are not yet available.…”