Computational algorithms for aerodynamic analysis and design
Applied Numerical Mathematics
High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
Multidimensional flux-limited advection schemes
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Flux correction tools for finite elements
Journal of Computational Physics
On the design of general-purpose flux limiters for finite element schemes. I. Scalar convection
Journal of Computational Physics
Monoslope and multislope MUSCL methods for unstructured meshes
Journal of Computational Physics
Image Sequence Interpolation Using Optimal Control
Journal of Mathematical Imaging and Vision
New robust nonconforming finite elements of higher order
Applied Numerical Mathematics
Mixed element FEM level set method for numerical simulation of immiscible fluids
Journal of Computational Physics
Hi-index | 31.46 |
A new approach to the derivation of local extremum diminishing finite element schemes is presented. The monolonicity of the Galerkin discretization is enforced by adding discrete diffusion so as to eliminate all negative off-diagonal matrix entries. The resulting low-order operator of upwind type acts as a preconditioner within an outer defect corpection loop. A generalization of TVD concepts is employed to design solution-dependent antidiffusive fluxes which are inserted into the defect vector to preclude excessive smearing of solution profiles by numerical diffusion. Standard TVD limiters can be applied edge-by-edge using a special reconstruction of local three-point stencils. As a fully multidimensional alternative to this technique, a new limiting strategy is introduced. A node-oriented flux limiter is constructed so as to control the ratio of upstream and downstream edge contributions which are associated with the positive and negative off-diagonal coefficients of the high-order transport operator, respectively. The proposed algorithm can be readily incorporated into existing flow solvers as a 'black-box' postprocessing tool for the matrix assembly routine. Its performance is illustrated by a number of numerical examples for scalar convection problems and incompressible flows in two and three dimensions.