1,473 research outputs found
Robust error estimates in weak norms for advection dominated transport problems with rough data
We consider mixing problems in the form of transient convection--diffusion
equations with a velocity vector field with multiscale character and rough
data. We assume that the velocity field has two scales, a coarse scale with
slow spatial variation, which is responsible for advective transport and a fine
scale with small amplitude that contributes to the mixing. For this problem we
consider the estimation of filtered error quantities for solutions computed
using a finite element method with symmetric stabilization. A posteriori error
estimates and a priori error estimates are derived using the multiscale
decomposition of the advective velocity to improve stability. All estimates are
independent both of the P\'eclet number and of the regularity of the exact
solution
A reduced basis super-localized orthogonal decomposition for reaction-convection-diffusion problems
This paper presents a method for the numerical treatment of
reaction-convection-diffusion problems with parameter-dependent coefficients
that are arbitrary rough and possibly varying at a very fine scale. The
presented technique combines the reduced basis (RB) framework with the recently
proposed super-localized orthogonal decomposition (SLOD). More specifically,
the RB is used for accelerating the typically costly SLOD basis computation,
while the SLOD is employed for an efficient compression of the problem's
solution operator requiring coarse solves only. The combined advantages of both
methods allow one to tackle the challenges arising from parametric
heterogeneous coefficients. Given a value of the parameter vector, the method
outputs a corresponding compressed solution operator which can be used to
efficiently treat multiple, possibly non-affine, right-hand sides at the same
time, requiring only one coarse solve per right-hand side.Comment: 27 pages, 6 figure
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
Computational modelling of iron-ore mineralisation with stratigraphic permeability anisotropy
This study develops a computational framework to model fluid transport in sedimentary basins, targeting iron ore deposit formation. It offers a simplified flow model, accounting for geological features and permeability anisotropy as driving factors. A new finite element method lessens computational effort, facilitating robust predictions and cost-effective exploration. This methodology, applicable to other mineral commodities, enhances understanding of genetic models, supporting the search for new mineral deposits amid the global energy transition
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