A MEEVC discretization for two-dimensional incompressible Navier-Stokes equations with general boundary conditions

In this work, we present a mass, energy, enstrophy and vorticity conserving (MEEVC) mixed finite element discretization for two-dimensional incompressible Navier-Stokes equations as an alternative to the original MEEVC scheme proposed in A. Palha and M. Gerritsma (2017) [5]. The present method can incorporate general boundary conditions....

Structure-Preserving Hyper-Reduction Methods for the Incompressible Navier-Stokes Equations

In this master thesis several novel DEIM formulations are proposed that enable the construction of non-linearly stable hyper-reduced order models (hROMs) of the incompressible Navier-Stokes equations. The hROMs have the same mass, momentum and energy conservation properties as the previously proposed ROM, but they do not suffer of prohibitively...

Mimetic Spectral Element Method and Extensions toward Higher Computational Efficiency

Structure-conserving numerical methods that aim at preserving certain structures of the PDEs at the discrete level have been an interesting research topic for many decades. The mimetic spectral element method, a recently developed arbitrary order structure-preserving method on orthogonal or curvilinear meshes, has also been drawing increasingly...

Process Intensification of Mesoporous Material's Synthesis by Microwave-Assisted Surfactant Removal

Mesoporous materials are of vital importance for use in separation, adsorption, and catalysis. The first step in their preparation consists of synthesizing an organic-inorganic hybrid in which a structuring directing agent (SDA, normally a surfactant) is used to provide the desired porosity. The most common method to eliminate the SDA, and...

Bas-Relief Modeling from Normal Layers

Bas-relief is characterized by its unique presentation of intrinsic shape properties and/or detailed appearance using materials raised up in different degrees above a background. However, many bas-relief modeling methods could not manipulate scene details well. We propose a simple and effective solution for two kinds of bas-relief modeling (i...

A mimetic spectral element method for the 2D incompressible Navier-Stokes equations

Structure Preserving Isogeometric Analysis for Computational Fluid Dynamics

Double degree. Supervision of the thesis also at: Faculty Applied Mathematics, Department Numerical Analysis, Programme M.Sc. Applied Mathematics. Structure-preserving discretization techniques preserve fundamental structure of operators and operands found in partial differential equations. Classical discretization techniques sometimes neglect...

Investigation of Accuracy, Speed and Stability of Hyper-Reduction Techniques for Nonlinear FE

The field of Hyper-reduction for Nonlinear Finite Element Method attempts to address the large durations due to repeated evaluation and assembly of the internal force and Jacobian. Stability, accuracy and speed are three aspects of thesemethods that has been dealt with in this thesis. There are two methods that are popular within the...

Hamiltonian Discontinuous Galerkin Finite Element Method for Internal Gravity Waves: An exactly energy conserving discretization

A DGFEM discretization has been developed for the Hamiltonian dynamics of stratified incompressible linear fluid flow. The developed discretization can handle the numerical challenges posed by wave attractors: the three dimensionality of the domain, the focusing of wave energy and the incompressibility of the flow. The discretization is...