@Article{CiCP-31-1,
author = {Khouya, Bassou and Mofdi, El-Amrani,  and Seaid, Mohammed},
title = {A Conservative and Monotone Characteristic Finite Element Solver for Three-Dimensional Transport and Incompressible Navier-Stokes Equations on Unstructured Grids},
journal = {Communications in Computational Physics},
year = {2022},
volume = {31},
number = {1},
pages = {224--256},
abstract = {<p style="text-align: justify;">We propose a mass-conservative and monotonicity-preserving characteristic finite element method for solving three-dimensional transport and incompressible
Navier-Stokes equations on unstructured grids. The main idea in the proposed algorithm consists of combining a mass-conservative and monotonicity-preserving modified method of characteristics for the time integration with a mixed finite element
method for the space discretization. This class of computational solvers benefits from
the geometrical flexibility of the finite elements and the strong stability of the modified method of characteristics to accurately solve convection-dominated flows using
time steps larger than its Eulerian counterparts. In the current study, we implement
three-dimensional limiters to convert the proposed solver to a fully mass-conservative
and essentially monotonicity-preserving method in addition of a low computational
cost. The key idea lies on using quadratic and linear basis functions of the mesh element where the departure point is localized in the interpolation procedures. The
proposed method is applied to well-established problems for transport and incompressible Navier-Stokes equations in three space dimensions. The numerical results
illustrate the performance of the proposed solver and support its ability to yield accurate and efficient numerical solutions for three-dimensional convection-dominated
flow problems on unstructured tetrahedral meshes.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2020-0229},
url = {https://global-sci.com/article/79511/a-conservative-and-monotone-characteristic-finite-element-solver-for-three-dimensional-transport-and-incompressible-navier-stokes-equations-on-unstructured-grids}
}