Related papers: Solving the six-dimensional Vlasov-Maxwell System …
Active Flux is a modified Finite Volume method that evolves additional Degrees of Freedom for each cell that are located on the interface by a non-conservative method to compute high-order approximations to the numerical fluxes through the…
The Active Flux (AF) method is a compact, high-order finite volume scheme that enhances flexibility by introducing point values at cell interfaces as additional degrees of freedom alongside cell averages. The method of lines is employed…
Active Flux (AF) is a recent numerical method for hyperbolic conservation laws, whose degrees of freedom are averages/moments and (shared) point values at cell interfaces. It has been noted previously in a heuristic fashion that it thus…
An advanced Volume of Fluid (VOF) method is presented that enables performant three-dimensional Direct Numerical Simulations (DNS) of the interaction of two immiscible fluids in a gaseous environment with large topology changes, e.g.,…
The Active Flux (AF) is a compact, high-order finite volume scheme that allows more flexibility by introducing additional point value degrees of freedom at cell interfaces. This paper proposes a positivity-preserving (PP) AF scheme for…
Kinetic equations are difficult to solve numerically due to their high dimensionality. A promising approach for reducing computational cost is the dynamical low-rank algorithm, which decouples the dimensions of the phase space by proposing…
Active Flux is an extension of the Finite Volume method and additionally incorporates point values located at cell boundaries. This gives rise to a globally continuous approximation of the solution. Originally, the Active Flux method…
The Active Flux scheme is a finite volume scheme with additional point values distributed along the cell boundary. It is third order accurate and does not require a Riemann solver. Instead, given a reconstruction, the initial value problem…
Validity of fluid models breaks down for non-thermal or weakly collisional plasmas which often occur e.g. in the solar wind. In these regimes one has to resort to modelling through the first-principle Vlasov-Maxwell system, but its…
The Active Flux scheme is a Finite Volume scheme with additional degrees of freedom. It makes use of a continuous reconstruction and does not require a Riemann solver. An evolution operator is used for the additional degrees of freedom on…
This paper presents a grid-free simulation algorithm for the fully three-dimensional Vlasov--Poisson system for collisionless electron plasmas. We employ a standard particle method for the numerical approximation of the distribution…
The Active Flux method is a finite volume method for hyperbolic conservation laws that uses both cell averages and point values as degrees of freedom. Several versions of such methods are currently under development. We focus on third order…
The accurate representation of surface tension driven flows in multiphase systems is considered a challenging problem to resolve numerically. Although there have been extensive works in the past that have presented approaches to resolve…
This study proposes a novel adaptive finite volume-particle method (AFVPM) for accurate and efficient free surface flow simulations. The proposed AFVPM synergistically combines the Eulerian finite volume method (FVM) on unstructured meshes…
The Active Flux scheme is a Finite Volume scheme with additional point values distributed along the cell boundary. It is third order accurate and does not require a Riemann solver: the continuous reconstruction serves as initial data for…
The complexity of binary droplet collisions increases for the collision of immiscible liquids with the occurrence of triple lines and thin encapsulating films. The Volume of Fluid (VOF) method is extended with an efficient interface…
The dynamics of collisionless plasmas can be modelled by the Vlasov-Maxwell system of equations. An Eulerian approach is needed to accurately describe processes that are governed by high energy tails in the distribution function, but is of…
Finite volume schemes for hyperbolic conservation laws require a numerical intercell flux. In one spatial dimension the numerical flux can be successfully obtained by solving (exactly or approximately) Riemann problems that are introduced…
This paper studies the active flux (AF) methods for two-dimensional hyperbolic conservation laws, focusing on the flux vector splitting (FVS) for the point value update and bound-preserving (BP) limitings, which is an extension of our…
The active flux (AF) method is a compact high-order finite volume method originally proposed for solving hyperbolic conservation laws, in which cell averages and point values at cell interfaces are evolved simultaneously. This paper…