Low-diffusivity scalar transport using a WENO scheme and dual meshing

Interfacial mass transfer of low-diffusive substances in an unsteady flow environment is marked by a very thin boundary layer at the interface and other regions with steep concentration gradients. A numerical scheme capable of resolving accurately most details of this process is presented. In this scheme, the fourth-order accurate WENO method developed by Liu et al. (1994) was implemented on a non-uniform staggered mesh to discretize the scalar convection while for the scalar diffusion a fourth-order accurate central discretization was employed. The discretization of the scalar convection-diffusion equation was combined with a fourth-order Navier-Stokes solver which solves the incompressible flow. A dual meshing strategy was employed, in which the scalar was solved on a finer mesh than the incompressible flow. The solver was tested by performing a number of two-dimensional simulations of an unstably stratified flow with low diffusivity scalar transport. The unstable stratification led to buoyant convection which was modelled using a Boussinesq approximation with a linear relationship between flow temperature and density. The order of accuracy for one-dimensional scalar transport on a stretched and uniform grid was also tested. The results show that for the method presented above a relatively coarse mesh is sufficient to accurately describe the fluid flow, while the use of a refined mesh for the low-diffusive scalars is found to be beneficial in order to obtain a highly accurate resolution with negligible numerical diffusion

A Multiscale Thermo-Fluid Computational Model for a Two-Phase Cooling System

In this paper, we describe a mathematical model and a numerical simulation method for the condenser component of a novel two-phase thermosyphon cooling system for power electronics applications. The condenser consists of a set of roll-bonded vertically mounted fins among which air flows by either natural or forced convection. In order to deepen the understanding of the mechanisms that determine the performance of the condenser and to facilitate the further optimization of its industrial design, a multiscale approach is developed to reduce as much as possible the complexity of the simulation code while maintaining reasonable predictive accuracy. To this end, heat diffusion in the fins and its convective transport in air are modeled as 2D processes while the flow of the two-phase coolant within the fins is modeled as a 1D network of pipes. For the numerical solution of the resulting equations, a Dual Mixed-Finite Volume scheme with Exponential Fitting stabilization is used for 2D heat diffusion and convection while a Primal Mixed Finite Element discretization method with upwind stabilization is used for the 1D coolant flow. The mathematical model and the numerical method are validated through extensive simulations of realistic device structures which prove to be in excellent agreement with available experimental data

Primal dual mixed finite element methods for indefinite advection--diffusion equations

We consider primal-dual mixed finite element methods for the advection--diffusion equation. For the primal variable we use standard continuous finite element space and for the flux we use the Raviart-Thomas space. We prove optimal a priori error estimates in the energy- and the $L^2$-norms for the primal variable in the low Peclet regime. In the high Peclet regime we also prove optimal error estimates for the primal variable in the $H(div)$ norm for smooth solutions. Numerically we observe that the method eliminates the spurious oscillations close to interior layers that pollute the solution of the standard Galerkin method when the local Peclet number is high. This method, however, does produce spurious solutions when outflow boundary layer presents. In the last section we propose two simple strategies to remove such numerical artefacts caused by the outflow boundary layer and validate them numerically.Comment: 25 pages, 6 figures, 5 table

A Mixed Hybrid Finite Volume Scheme for Incompressible Navier-Stokes

Mixed Virtual Elements (MVE) is an innovative class of discretization schemes allowing solution of PDEs on virtually any mesh; such schemes stem from the idea of building discrete operators mimicking certain key properties of their continuous counterparts. In our previous work [27] we implemented our own 1st-order MVE scheme for convection-diffusion. In the present work, a) we extend such scheme to formally 2nd-order accuracy, b) we deal with the subsequent stability issues, c) we derive a full formally 2nd-order MVE scheme for incompressible steady-state Navier-Stokes, d) we provide a first suggestion for a MVE N-S solution algorithm. Numerical results are reported for benchmark test cases