4,883 research outputs found
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
-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 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 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
- …