41 research outputs found
On an unconditionally convergent stabilized finite element approximation of resistive magnetohydrodynamics
In this work, we propose a new stabilized finite element formulation for the approximation of the
resistive magnetohydrodynamics equations. The novelty of this formulation with respect to existing
ones is the fact that it always converges to the physical solution, even for singular ones. We have performed
a detailed stability and convergence analysis of the formulation in a simplified setting. From
the convergence analysis, we infer that a particular type of meshes with a macro-element structure is
needed, which can be easily obtained after a straight modification of any original mesh. A detailed
set of numerical experiments have been performed in order to validate our approach.Peer ReviewedPreprin
A Penalty-projection based Efficient and Accurate Stochastic Collocation Method for Magnetohydrodynamic Flows
We propose, analyze, and test a penalty projection-based efficient and
accurate algorithm for the Uncertainty Quantification (UQ) of the
time-dependent Magnetohydrodynamic (MHD) flow problems in convection-dominated
regimes. The algorithm uses the Els\"asser variables formulation and discrete
Hodge decomposition to decouple the stochastic MHD system into four
sub-problems (at each time-step for each realization) which are much easier to
solve than solving the coupled saddle point problems. Each of the sub-problems
is designed in a sophisticated way so that at each time-step the system matrix
remains the same for all the realizations but with different right-hand-side
vectors which allows saving a huge amount of computer memory and computational
time. Moreover, the scheme is equipped with ensemble eddy-viscosity and
grad-div stabilization terms. The stability of the algorithm is proven
rigorously. We prove that the proposed scheme converges to an equivalent
non-projection-based coupled MHD scheme for large grad-div stabilization
parameter values. We examine how Stochastic Collocation Methods (SCMs) can be
combined with the proposed penalty projection UQ algorithm. Finally, a series
of numerical experiments are given which verify the predicted convergence
rates, show the algorithm's performance on benchmark channel flow over a
rectangular step, and a regularized lid-driven cavity problem with high random
Reynolds number and magnetic Reynolds number.Comment: 28 pages, 13 figure
Numerical study of heat source/sink effects on dissipative magnetic nanofluid flow from a non-linear inclined stretching/shrinking sheet
This paper numerically investigates radiative magnetohydrodynamic mixed convection boundary layer flow of nanofluids over a nonlinear inclined stretching/shrinking sheet in the presence of heat source/sink and viscous dissipation. The Rosseland approximation is adopted for thermal radiation effects and the Maxwell-Garnetts and Brinkman models are used for the effective thermal conductivity and dynamic viscosity of the nanofluids respectively. The governing coupled nonlinear momentum and thermal boundary layer equations are rendered into a system of ordinary differential equations via local similarity transformations with appropriate boundary conditions. The non-dimensional, nonlinear, well-posed boundary value problem is then solved with the Keller box implicit finite difference scheme. The emerging thermo-physical dimensionless parameters governing the flow are the magnetic field parameter, volume fraction parameter, power-law stretching parameter, Richardson number, suction/injection parameter, Eckert number and heat source/sink parameter. A detailed study of the influence of these parameters on velocity and temperature distributions is conducted. Additionally the evolution of skin friction coefficient and Nusselt number values with selected parameters is presented. Verification of numerical solutions is achieved via benchmarking with some limiting cases documented in previously reported results, and generally very good correlation is demonstrated. This investigation is relevant to fabrication of magnetic nanomaterials and high temperature treatment of magnetic nano-polymers
Status of research at the Institute for Computer Applications in Science and Engineering (ICASE)
Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis and computer science is summarized