3DFLUX: a high-order fully three-dimensional flux integral solver for the scalar transport equation. 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.

Keywords for this software

Anything in here will be replaced on browsers that support the canvas element