The MAST FV/FE scheme for the simulation of two-dimensional thermohaline processes in variable-density saturated porous media

Advances in Water Resources

Begnudelli

et al. 2011

108

This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues.Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. The governing Partial Differential Equations are discretized using a procedure similar to the linear conforming Finite Element Galerkin scheme, with a different flux formulation and a special flux treatment that requires Delaunay triangulation but entire solution monotonicity. A simple mesh adjustment is suggested, that attains the Delaunay condition for all the triangle sides without changing the original nodes location and also maintains the internal boundaries. The original governing system is solved applying a fractional time step procedure, that solves consecutively a convective prediction system and a diffusive correction system. The non linear components of the problem are concentrated in the prediction step, while the correction step leads to the solution of a linear system of the order of the number of computational cells. A semi-analytical procedure is applied for the solution of the prediction step. The discretized formulation of the governing equations allows to handle also wetting and drying processes without any additional specific treatment. Local energy dissipations, mainly the effect of vertical walls and hydraulic jumps, can be easily included in the model.Several numerical experiments have been carried out in order to test (1) the stability of the proposed model with regard to the size of the Courant number and to the mesh irregularity, (2) its computational performance, (3) the convergence order by means of mesh refinement. The model results are also compared with the results obtained by a fully dynamic model. Finally, the application to a real field case with a Venturi channel is presented.

show abstract

Section: Introductionmentioning

confidence: 99%

MAST-2D diffusive model for flood prediction on domains with triangular Delaunay unstructured meshes

Advances in Water Resources

Begnudelli

et al. 2011

108

show abstract

“…In figure 10,j, for case 12 (ε = 0.75, ϕ = -π /4), the combined effects of the same direction of the rotation of the inner cylinder and of the buoyancy force on the left side of the same cylinder, as well as the anticlockwise rotation of the outer cylinder, lead to the maximum Nu out value around ϕ = 2π. During the TCS, due to the lack of nodes outside the domain, we do not compute any corrective thermal flux component orthogonal to those walls (see also [43] and cited references). As ICs we set zero pressure, temperature and velocity.…”

Section: Mixed Convection In Eccentric Annulimentioning

confidence: 99%

A new solver for incompressible non-isothermal flows in natural and mixed convection over unstructured grids

Applied Mathematical Modelling

Driss

et al. 2022

Self Cite

“…The CPU time relative to the convective step is almost independent on the mesh elements number, since this represents the ''explicit'' component of the method. The small decrement of the average CPU time of the convective component can be related to the increasing CFL numbers obtained by partitioning and to the best aptitude of the algorithm to work with CFL numbers greater than one [3][4][5][6]. The CPU time per single cell required for the solution of the diffusive linear system increases with the element number.…”

Section: Test 4 Computational Cost Investigationmentioning

confidence: 99%

“…The prediction step is solved applying the MArching in Space and Time (MAST) methodology, recently proposed for the solution of advection dominated problems [2,7], fully dynamic shallow waters equations [3,4], diffusive form of the shallow waters equations [6], as well as transport problems in saturated porous media with variable density [5]. The requirement for the application of the MAST methodology is the existence of an exact or approximated scalar potential for the flow field.…”

Section: Introductionmentioning

confidence: 99%

The MAST-edge centred lumped scheme for the flow simulation in variably saturated heterogeneous porous media

Journal of Computational Physics

Tucciarelli

2012

Self Cite