Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 5198884567, ext. 32700
Fax: 5197464319
PDF files require Adobe Acrobat Reader
M3 4001
Keegan Kirk  Applied Math, University of Waterloo
Analysis of Spacetime Hybridizable Discontinuous Galerkin Methods for Incompressible Flows on Moving Domains
Many industrial problems require the solution of timedependent partial differential equations on moving and deforming domains. Notable examples include the simulation of rotating wind turbines in strong air flow, wave impact on offshore structures, and arterial blood flow in the human body. In contrast to problems posed on fixed domains, numerical methods for moving domains must satisfy the Geometric Conservation Law (GCL), a nontrivial feat.
A viable candidate that automatically satisfies the GCL is the spacetime discontinuous Galerkin (DG) method, which makes no distinction between spatial and temporal variables. Spacetime DG is well suited to handle moving and deforming domains but at a significant increase in computational cost in comparison to traditional timestepping methods. Attempts to rectify this situation have led to the pairing of spacetime DG with the hybridizable discontinuous Galerkin (HDG) method, which was developed solely to reduce the computational expense of DG. The combination of the two methods results in a scheme that retains the highorder spatial and temporal accuracy and geometric flexibility of spacetime DG without the associated computational burden.
This talk will comprise of three parts. We first discuss the error analysis of a spacetime HDG method for the advectiondiffusion problem on moving domains. Next, we will introduce pressurerobustness and prove pressurerobust error estimates for an HDG method for the steadystate incompressible NavierStokes equations. Lastly, we discuss a pressurerobust spacetime HDG method for the timedependent incompressible NavierStokes equations on moving domains and touch on some challenges in its analysis.
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Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 5198884567, ext. 32700
Fax: 5197464319
PDF files require Adobe Acrobat Reader
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