Mimicking of Non-conservative Systems: Demonstration of a generalized method for applying the mimetic spectral element method to non-conservative systems

The mimetic spectral element method is a relatively young method in numerical solutions of partial differential equations and actions that describe physical systems. Its advantage is that it takes the geometrical structure of the problem into account which guarantees consistency of the numerical scheme and the conservation of relevant quantities...

Spatially mass-, kinetic energy- and helicity-preserving mimetic discretization of 3D incompressible Euler flows

Based on the recently developed mimetic spectral element method, we propose an effective numerical scheme for solving three-dimensional periodic incompressible Euler flows, which spatially preserves mass, kinetic energy and helicity. Preserving multiple integral invariants numerically will significantly contribute to the stability and accuracy...

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...