We present a discrete Hodge-Morrey-Friedrichs decomposition for piecewise constant vector fields on simplicial surfaces with boundary which is structurally consistent with the smooth theory. In particular, it preserves a deep linkage between metric properties of the spaces of harmonic Dirichlet and Neumann fields and the topology of the underlying geometry, which reveals itself as a discrete de...

In this article we present a dissipative definition of a solution for initial boundary value problems for Friedrichs’ systems posed in the space Lt,x. We study the information contained in this definition and prove an existence and uniqueness theorem in the non-characteristic case and with constant coefficients. Finally, we compare our choice of boundary condition to previous works, especially ...

We present a new numerical method to solve the Vlasov-Darwin and Vlasov-Poisswell systems which are approximations of the Vlasov-Maxwell equation in the asymptotic limit of the infinite speed of light. These systems model low-frequency electromagnetic phenomena in plasmas, and thus “light waves” are somewhat supressed, which in turn allows the numerical discretization to dispense with the Coura...

A semi-Lagrangian scheme is applied for the first time to computations of charged particle motions along magnetic field lines, to numerically solve the δf gyrokinetic equations in a flux tube geometry. This new solver adopted in the gyrokinetic Vlasov simulations has an advantage over the conventional Eulerian codes in calculating the parallel dynamics, because semi-Lagrangian schemes are free ...

This Letter reports a validation of lattice-Boltzmann approach following the Taylor–Green Vortex benchmark presented at 19th International Congress on Numerical Combustion and recently reported by Abdelsamie et al. [“The vortex as for high-fidelity combustion simulations using low-Mach solvers,” Comput. Fluids 223, 104935 (2021)]. The approach, despite having time step bound an acoustic Courant...