De Angelis, Enrico Maria (2018) Development of a high-order parallel solver for direct and large eddy simulations of turbulent flows. [Tesi di dottorato]


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Item Type: Tesi di dottorato
Title: Development of a high-order parallel solver for direct and large eddy simulations of turbulent flows
De Angelis, Enrico
Date: 7 December 2018
Number of Pages: 146
Institution: Università degli Studi di Napoli Federico II
Department: Ingegneria Industriale
Dottorato: Ingegneria industriale
Ciclo di dottorato: 31
Coordinatore del Corso di dottorato:
Coppola, GennaroUNSPECIFIED
Capuano, FrancescoUNSPECIFIED
Date: 7 December 2018
Number of Pages: 146
Uncontrolled Keywords: computational fluid dynamics, direct numerical simulation, large eddy simulation, compact finite difference schemes, parallel computing, three-dimensional, domain decomposition, Fortran, MPI
Settori scientifico-disciplinari del MIUR: Area 01 - Scienze matematiche e informatiche > INF/01 - Informatica
Area 09 - Ingegneria industriale e dell'informazione > ING-IND/06 - Fluidodinamica
Date Deposited: 02 Jan 2019 15:14
Last Modified: 29 Jun 2020 10:56


Turbulence is inherent in fluid dynamics, in that laminar flows are rather the exception than the rule, hence the longstanding interest in the subject, both within the academic community and the industrial R&D laboratories. Since 1883, much progress has been made, and statistics applied to turbulence have provided understanding of the scaling laws which are peculiar to several model flows, whereas experiments have given insight on the structure of real-world flows, but, soon enough, numerical approaches to the matter have become the most promising ones, since they lay the ground for the solution of high Reynolds number unsteady Navier-Stokes equations by means of computer systems. Nevertheless, despite the exponential rise in computational capability over the last few decades, the more computer technology advances, the higher the Reynolds number sought for test-cases of industrial interest: there is a natural tendency to perform simulations as large as possible, a habit that leaves no room for wasting resources. Indeed, as the scale separation grows with Re, the reduction of wall clock times for a high-fidelity solution of desired accuracy becomes increasingly important. To achieve this task, a CFD solver should rely on the use of appropriate physical models, consistent numerical methods to discretize the equations, accurate non-dissipative numerical schemes, efficient algorithms to solve the numerics, and fast routines implementing those algorithms. Two archetypal approaches to CFD are direct and large-eddy simulation (DNS and LES respectively), which profoundly differ in several aspects but are both “eddy-resolving” methods, meant to resolve the structures of the flow-field with the highest possible accuracy and putting in as little spurious dissipation as possible. These two requirements of accurate resolution of scales, and energy conservation, should be addressed by any numerical method, since they are essential to many real-world fluid flows of industrial interest. As a consequence, high order numerical schemes, and compact schemes among them, have received much consideration, since they address both goals, at the cost of a lower ease of application of the boundary condition, and a higher computational cost. The latter problem is tackled with parallel computing, which also allows to take advantage of the currently available computer power at the best possible extent. The research activity conducted by the present author has concerned the development, from scratch, of a three-dimensional, unsteady, incompressible Navier-Stokes parallel solver, which uses an advanced algorithm for the process-wise solution of the linear systems arising from the application of high order compact finite difference schemes, and hinges upon a three-dimensional decomposition of the cartesian computational space. The code is written in modern Fortran 2003 — plus a few features which are unique to the 2008 standard — and is parallelized through the use of MPI 3.1 standard’s advanced routines, as implemented by the OpenMPI library project. The coding was carried out with the objective of creating an original CFD high-order parallel solver which is maintainable and extendable, of course within a well-defined range of possibilities. With this main priority being outlined, particular attention was paid to several key concepts: modularity and readability of the source code and, in turn, its reusability; ease of implementation of virtually any new explicit or implicit finite difference scheme; modern programming style and avoidance of deprecated old legacy Fortran constructs and features, so that the world wide web is a reliable and active means to the quick solution of coding problems arising from the implementation of new modules in the code; last but not least, thorough comments, especially in critical sections of the code, explaining motives and possible expected weak links. Design, production, and documentation of a program from scratch is almost never complete. This is certainly true for the present effort. The method and the code are verified against the full three-dimensional Lid-Driven Cavity and Taylor-Green Vortex flows. The latter test is used also for the assessment of scalability and parallel efficiency.


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