Discretization of transport equations on 2D Cartesian unstructured grids using data from remote cells for the convection terms

Abstract

SUMMARYThis paper presents a new ÿnite volume discretization methodology for the solution of transport equations on locally reÿned or unstructured Cartesian meshes. The implementation of the cell-face values of the dependent variables enables the employment of data from remote cells and thus the use of higherorder di erencing schemes. It also results in simple and ux-conservative multiple-scale stencils for the discretization of the governing equations. The latter are ÿnally cast into a generalized form that does not depend on the local mesh structure. The performance of the numerical model is demonstrated on some classical 2D problems using various gridding techniques and a bounded second-order upwind scheme. A stable and e cient behaviour of the algorithm is observed in all test cases. The results indicate that the combination in the present model of both local grid reÿnement and second-order discretization can produce substantially more accurate solutions than each of the above techniques alone, for the same computational e ort. The method is also applicable to turbulent ows and can be easily extended to three-dimensions.

Unstructured Cartesian refinement with sharp interface immersed boundary method for 3D unsteady incompressible flows

“…Papadakis and Bergeles [48] extended the work of [19] and introduced a low-order fully unstructured method for solving 3D turbulent incompressible flows, covering the computational domain by block-structured subgrids. Inspired from the previous works, Anagnostopoulos [1] discretized the transport equations on arbitrary refined 2D Cartesian grids, satisfying, at the same time, the divergence free constraint. Recently, Angelidis et al [2] presented a 2D fully unstructured Cartesian incompressible flow solver to investigate laminar canonical flows and the turbulent air mixing potential in idealized street canyons for several thermal stratification scenarios [45].…”

Αριθμητική Μεθοδολογία Προσομοίωσης Της Ροής Και Εναλλαγής Ενέργειας Σε Υδροστροβίλους Δράσης, Με Πειραματική Διερεύνηση Και Πιστοποιήση

“…Όπως αναφέρθηκε, η Εξίσωση (3.7) δίνει μόνο μια αρχική εκτίμηση της νέας θέσης του σωματιδίου μετά από χρονικό διάστημα δt. Για τον λόγο αυτόν εφαρμόζεται στη συνέχεια ένα σχήμα Πρόβλεψης-Διόρθωσης δεύτερης τάξης ακριβείας [72]. Με την εφαρμογή του συγκεκριμένου σχήματος υπολογίζεται η τελική θέση του σωματιδίου με μεγαλύτερη ακρίβεια, ενώ η διαδικασία αυτή επαναλαμβάνεται σε κάθε χρονικό βήμα ολοκλήρωσης.…”