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 language | English |
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Title of host publication | Application of Mathematics in Technical and Natural Sciences |
Subtitle of host publication | 8th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2016 |
Publisher | American Institute of Physics Inc. |
Volume | 1773 |
ISBN (Electronic) | 9780735414310 |
DOIs | |
Publication status | Published - 13 Oct 2016 |
Event | 8th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2016 - Albena, Bulgaria Duration: 22 Jun 2016 → 27 Jun 2016 |
Other
Other | 8th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2016 |
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Country/Territory | Bulgaria |
City | Albena |
Period | 22/06/16 → 27/06/16 |