The node-centred finite volume approach: bridge between finite differences and finite elements
Computer Methods in Applied Mechanics and Engineering
Flux correction tools for finite elements
Journal of Computational Physics
Explicit and implicit FEM-FCT algorithms with flux linearization
Journal of Computational Physics
Anderson Acceleration for Fixed-Point Iterations
SIAM Journal on Numerical Analysis
Linearity-preserving flux correction and convergence acceleration for constrained Galerkin schemes
Journal of Computational and Applied Mathematics
| Hi-index | 7.29 |
Convection of a scalar quantity by a compressible velocity field may give rise to unbounded solutions or nonphysical overshoots at the continuous and discrete level. In this paper, we are concerned with solving continuity equations that govern the evolution of volume fractions in Eulerian models of disperse two-phase flows. An implicit Galerkin finite element approximation is equipped with a flux limiter for the convective terms. The fully multidimensional limiting strategy is based on a flux-corrected transport (FCT) algorithm. This nonlinear high-resolution scheme satisfies a discrete maximum principle for divergence-free velocities and ensures positivity preservation for arbitrary velocity fields. To enforce an upper bound that corresponds to the maximum-packing limit, an FCT-like overshoot limiter is applied to the converged convective fluxes at the end of each time step. This postprocessing step imposes an additional physical constraint on the numerical solution to the unconstrained mathematical model. Numerical results for 2D implosion problems illustrate the performance of the proposed limiting procedure.