A mass, energy, enstrophy and vorticity conserving (MEEVC) mimetic spectral element discretization for the 2D incompressible Navier–Stokes equations
A Palha, M Gerritsma - Journal of Computational Physics, 2017 - Elsevier
In this work we present a mimetic spectral element discretization for the 2D incompressible
Navier–Stokes equations that in the limit of vanishing dissipation exactly preserves mass …
Navier–Stokes equations that in the limit of vanishing dissipation exactly preserves mass …
Petrov–Galerkin flux upwinding for mixed mimetic spectral elements, and its application to geophysical flow problems
D Lee - Computers & Mathematics with Applications, 2021 - Elsevier
Upwinded mass fluxes are described and analysed for advection operators discretised
using mixed mimetic spectral elements. This involves a Petrov–Galerkin formulation by …
using mixed mimetic spectral elements. This involves a Petrov–Galerkin formulation by …
Vertex-based compatible discrete operator schemes on polyhedral meshes for advection-diffusion equations
P Cantin, A Ern - Computational Methods in Applied Mathematics, 2016 - degruyter.com
We devise and analyze vertex-based, Péclet-robust, lowest-order schemes for advection-
diffusion equations that support polyhedral meshes. The schemes are formulated using …
diffusion equations that support polyhedral meshes. The schemes are formulated using …
Mimetic spectral element method for anisotropic diffusion
M Gerritsma, A Palha, V Jain, Y Zhang - … Methods for PDEs: State of the …, 2018 - Springer
This chapter addresses the topological structure of steady, anisotropic, inhomogeneous
diffusion problems. Differential operators are represented by sparse incidence matrices …
diffusion problems. Differential operators are represented by sparse incidence matrices …
Mixed mimetic spectral element method applied to Darcy's problem
PP Rebelo, A Palha, M Gerritsma - Spectral and High Order Methods for …, 2013 - Springer
We present a discretization for Darcy's problem using the recently developed Mimetic
Spectral Element Method (Kreeft et al.(2011) Mimetic framework on curvilinear …
Spectral Element Method (Kreeft et al.(2011) Mimetic framework on curvilinear …
A geometric approach towards momentum conservation
In this work, a geometric discretization of the Navier-Stokes equations is sought by treating
momentum as a covector-valued volume-form. The novelty of this approach is that we treat …
momentum as a covector-valued volume-form. The novelty of this approach is that we treat …
[HTML][HTML] Mimetic Spectral Element Method and Extensions toward Higher Computational Efficiency
Y Zhang - 2022 - research.tudelft.nl
Abstract 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 PDEs at the discrete level have been an interesting research topic for many decades …
High order methods with exact conservation properties
R Hiemstra, M Gerritsma - Spectral and High Order Methods for Partial …, 2013 - Springer
Conservation laws, in for example, electromagnetism, solid and fluid mechanics, allow an
exact discrete representation in terms of line, surface and volume integrals. In this paper, we …
exact discrete representation in terms of line, surface and volume integrals. In this paper, we …
Discrete Lie derivative
M Gerritsma, J Kunnen, B de Heij - Numerical Mathematics and Advanced …, 2016 - Springer
Convection is an important transport mechanism in physics. Especially, in fluid dynamics at
high Reynolds numbers this term dominates. Modern mimetic discretization methods …
high Reynolds numbers this term dominates. Modern mimetic discretization methods …