A discontinuous Galerkin method for unsteady two-dimensional convective flows

A. C. Aristotelous, N. C. Papanicolaou

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Title of host publicationApplication of Mathematics in Technical and Natural Sciences
Subtitle of host publication8th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2016
PublisherAmerican Institute of Physics Inc.
Volume1773
ISBN (Electronic)9780735414310
DOIs
Publication statusPublished - 13 Oct 2016
Event8th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2016 - Albena, Bulgaria
Duration: 22 Jun 201627 Jun 2016

Other

Other8th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2016
Country/TerritoryBulgaria
CityAlbena
Period22/06/1627/06/16

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