Document Type

Conference Proceeding

Publication Date

2016

Abstract

We develop a High-Order Symmetric Interior Penalty (SIP) Discontinuous Galerkin (DG) Finite Element Method (FEM) to investigate two-dimensional in space natural convective flows in a vertical cavity. The physical problem is modeled by a coupled nonlinear system of partial differential equations and admits various solutions including stable and unstable modes in the form of traveling and/or standing waves, depending on the governing parameters. These flows are characterized by steep boundary and internal layers which evolve with time and can be well-resolved by high-order methods that also are adept to adaptive meshing. The standard no-slip boundary conditions which apply on the lateral walls, and the periodic conditions prescribed on the upper and lower boundaries, present additional challenges. The numerical scheme proposed herein is shown to successfully address these issues and furthermore, large Prandtl number values can be handled naturally. Discontinuous source terms and coefficients are an innate feature of multiphase flows involving heterogeneous fluids and will be a topic of subsequent work. Spatially adaptive Discontinuous Galerkin Finite Elements are especially suited to such problems.

Publication Title

AIP Conference Proceedings

ISSN

0094-243X

Publisher

American Institute of Physics

Volume

1773

Issue

110002

First Page

110002-1

Last Page

110002-12

Book TItle

Applications of Mathematics in Technical and Natural Sciences (AMITANS '16)

Book Editor(s)

M.D. Todorov

Book Publisher

American Institute of Physics

Place of Publication

Melville, NY

DOI

10.1063/1.4965006

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