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We consider dynamical low-rank approximation (DLRA) for the numericalsimulation of Vlasov--Poisson equations based on separation of space andvelocity variables, as proposed in several recent works. The standard approachfor the time integration in the DLRA model uses a splitting of the tangentspace projector for the low-rank manifold according to the separated variables.It can also be modified to allow for rank-adaptivity. A less studied aspect isthe incorporation of boundary conditions in the DLRA model. We propose avariational formulation of the projector splitting which allows to handleinflow boundary conditions on spatial domains with piecewise linear boundary.Numerical experiments demonstrate the principle feasibility of this approach.

Dynamical low-rank approximation of the Vlasov-Poisson equation with piecewise linear spatial boundary