On computations of temperature dependent incompressible flows by high order methods

Abstract

Abstract. Parallel vortex shedding from the heated cylinder as dependent on the cylinder temperature is investigated in numerical simulation. The computational scheme for the system of the incompressible Navier-Stokes equations coupled with the heat equation is presented. The scheme is based on the mixed implicit-explicit solver of the third order and the spectral element method for the spatial approximation. The results are compared with the experiments for flow of air and water. The Strouhal-Prandtl-Reynolds relationship and evolution of the separation angle as dependence on the temperature is the final result of the computations.

Scheme for Evolutionary Navier-Stokes-Fourier System with Temperature Dependent Material Properties Based on Spectral/hp Elements

“…Its modification was used also to the incompressible Navier-Stokes-Fourier system with temperature dependent viscosity and thermal conductivity in [10]. Efficiency of the approach comes from the implicit-explicit (IMEX) formulation, which allows decoupling of the system.…”

“…Efficiency of the approach comes from the implicit-explicit (IMEX) formulation, which allows decoupling of the system. The main contribution of the present work, which is a continuation of [10], is in extension to the problems with temperature dependent density. However, the velocity divergence cannot be further neglected in the momentum balance, what is the substantial difference from the previously discussed models and algorithms.…”

“…Subscript n + 1 (or operator in square brackets with subscript) denotes evaluation at time t n+1 = t 0 +(n+1) t, where t is the discrete time step. Coefficients {α q } Q−1 q=0 , {β q } Q−1 q=0 and γ for particular Q can be found, e.g., in [10]. Henceforward, we use ' * ' in the superscript to denote extrapolation,…”

“…The variable density ρ = ρ(T ) acts in our scheme as an inverse value, c.f. (10), so the splitting is done accordingly.…”

“…The energy equation with temperature dependent thermal conductivity is strongly non-linear. We split the diffusion operator to the time independent and the variable part, following the technique shown for the velocity-correction (10). We setκ = 1 for simplicity and the discretized energy equation (1c) gets form…”