Computational algorithms for aerodynamic analysis and design
Applied Numerical Mathematics
High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
High resolution schemes for hyperbolic conservation laws
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
Flux correction tools for finite elements
Journal of Computational Physics
Discrete maximum principle for linear parabolic problems solved on hybrid meshes
Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
On the design of general-purpose flux limiters for finite element schemes. I. Scalar convection
Journal of Computational Physics
On discrete maximum principles for nonlinear elliptic problems
Mathematics and Computers in Simulation
Numerical Approximation of Partial Differential Equations
Numerical Approximation of Partial Differential Equations
Failsafe flux limiting and constrained data projections for equations of gas dynamics
Journal of Computational Physics
Journal of Computational Physics
On (essentially) non-oscillatory discretizations of evolutionary convection-diffusion equations
Journal of Computational Physics
Linearity-preserving flux correction and convergence acceleration for constrained Galerkin schemes
Journal of Computational and Applied Mathematics
A flux-corrected transport algorithm for handling the close-packing limit in dense suspensions
Journal of Computational and Applied Mathematics
Hierarchical slope limiting in explicit and implicit discontinuous Galerkin methods
Journal of Computational Physics
Hi-index | 31.47 |
A new approach to the design of flux-corrected transport (FCT) algorithms for continuous (linear/multilinear) finite element approximations of convection-dominated transport problems is pursued. The algebraic flux correction paradigm is revisited, and a family of nonlinear high-resolution schemes based on Zalesak's fully multidimensional flux limiter is considered. In order to reduce the cost of flux correction, the raw antidiffusive fluxes are linearized about an auxiliary solution computed by a high- or low-order scheme. By virtue of this linearization, the costly computation of solution-dependent correction factors is to be performed just once per time step, and there is no need for iterative defect correction if the governing equation is linear. A predictor-corrector algorithm is proposed as an alternative to the hybridization of high- and low-order fluxes. Three FEM-FCT schemes based on the Runge-Kutta, Crank-Nicolson, and backward Euler time-stepping are introduced. A detailed comparative study is performed for linear convection-diffusion equations.