Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Adaptive multiresolution schemes for shock computations
Journal of Computational Physics
High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
A high-resolution hybrid compact-ENO scheme for shock-turbulence interaction problems
Journal of Computational Physics
Flux-corrected transport I. SHASTA, a fluid transport algorithm that works
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
Conservative hybrid compact-WENO schemes for shock-turbulence interaction
Journal of Computational Physics
Journal of Computational Physics
Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters
SIAM Journal on Scientific Computing
High order Hybrid central-WENO finite difference scheme for conservation laws
Journal of Computational and Applied Mathematics
Journal of Computational Physics
An improvement on the positivity results for 2-stage explicit Runge-Kutta methods
Journal of Computational and Applied Mathematics
A class of deformational flow test cases for linear transport problems on the sphere
Journal of Computational Physics
Journal of Computational Physics
3DFLUX: A high-order fully three-dimensional flux integral solver for the scalar transport equation
Journal of Computational Physics
A conservative multi-tracer transport scheme for spectral-element spherical grids
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.48 |
An efficient method for scalar advection is developed that selectively preserves monotonicity. Monotonicity preservation is applied only where the scalar field is likely to contain discontinuities as indicated by significant grid-cell-to-grid-cell variations in a smoothness measure conceptually similar to that used in weighted essentially non-oscillatory (WENO) methods. In smooth regions, the numerical diffusion associated with monotonicity-preserving methods is avoided. The resulting method, while not globally monotonicity preserving, allows the full accuracy of the underlying advection scheme to be achieved in smooth regions. The violations of monotonicity that do occur are generally very small, as seen in the tests presented here. Strict positivity preservation may be effectively and efficiently obtained through an additional flux correction step. The underlying advection scheme used to test this methodology is a variant of the piecewise parabolic method (PPM) that may be applied to multi-dimensional problems using density-corrected dimensional splitting and permits stable semi-Lagrangian integrations using CFL numbers larger than one. Two methods for monotonicity preservation are used here: flux correction and modification of the underlying polynomial reconstruction.