Polynomial interpolation schemes for internal derivative distributions on structured grids
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
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Numerical solution of problems on unbounded domains. a review
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
SIAM Journal on Scientific Computing
A semi-Lagrangian high-order method for Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
A Semi-Lagrangian Method for Turbulence Simulations Using Mixed Spectral Discretizations
Journal of Scientific Computing
A Fourth Order Scheme for Incompressible Boussinesq Equations
Journal of Scientific Computing
A windowing method for periodic inflow/outflow boundary treatment of non-periodic flows
Journal of Computational Physics
High-order accurate implementation of solid wall boundary conditions in curved geometries
Journal of Computational Physics
Selective monotonicity preservation in scalar advection
Journal of Computational Physics
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Numerical Recipes 3rd Edition: The Art of Scientific Computing
A gradient-augmented level set method with an optimally local, coherent advection scheme
Journal of Computational Physics
Inverse Lax-Wendroff procedure for numerical boundary conditions of conservation laws
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.45 |
We present a detailed derivation of a high-order, fully three-dimensional, conservative, monotonicity preserving, flux integral method for the solution of the scalar transport equation. This algorithm, named 3DFLUX, produces highly accurate solutions that are nearly unaffected by numerical dissipation, at a realistic computational cost. The performance of 3DFLUX is characterized by means of several challenging multidimensional tests. 3DFLUX is nominally third-order in space and second-order in time, however, at low Courant numbers, it appears to be superconvergent and, depending on the problem solved, is fourth-order or higher in space. Finally, 3DFLUX is used to simulate advection-diffusion of a complex temperature field in an incompressible turbulent flow of practical relevance, and its results are in excellent agreement with experimental measurements.