ADER scheme for incompressible Navier-Stokes equations on Overset grids with a compact transmission condition

A space-time Finite Volume method is devised to simulate incompressible viscous flows in an evolving domain. Inspired by the ADER method, the Navier-Stokes equations are discretized onto a space-time overset grid which is able to take into account both the shape of a possibly moving object and the evolution of the domain. A compact transmission condition is employed in order to mutually exchange information from one mesh to the other. The resulting method is second order accurate in space and time for both velocity and pressure. The accuracy and efficiency of the method are tested through reference simulations.Une méthode des volumes finis spatio-temporels est conçue pour simuler des écoulements visqueux incompressibles dans un domaine évolutif. Inspirée de la méthode ADER, les équations de Navier-Stokes sont discrétisées sur un maillage spatio-temporel overset qui est capable de prendre en compte à la fois la forme d’un objet éventuellement en mouvement et l’évolution du domaine. Une condition de transmission compacte est employée afin d’échanger mutuellement des informations d’un maillage à l’autre. La méthode résultante est d’une précision de second ordre dans l’espace et dans le temps pour la vitesse et la pression. La précision et l’efficacité de la méthode sont testées sur des cas test pris de la littérature

Numerical Simulation of Vortex-Induced Vibrations of Riser-Conductor Systems Including Soil-Structure Interactions

A fully three-dimensional numerical approach for analyzing deepwater drilling riser-conductor system vortex-induced vibrations (VIV) including soil-structure interactions (SSI) is presented. The drilling riser-conductor system is modeled as a tensioned beam with linearly distributed tension and is solved by a fully implicit discretization scheme. The fluid field around the riser-conductor system is obtained by Finite-Analytic Navier-Stokes (FANS) code, which numerically solves the unsteady Navier-Stokes equations. The SSI is taken into account by modeling the lateral soil resistance force according to p-y curves. Overset grid method is adopted to mesh the fluid domain with approximately 0.86 million computational points in total. Meshes are much finer in regions close to the pipe outer boundary and coarser in the far-field regions. A partitioned Fluid-Structure Interaction (FSI) method is achieved by communication between the fluid solver and pipe motion solver. A pipe VIV simulation without SSI is firstly presented and served as a benchmark case for following simulations. Two SSI models based on a popular p-y curve are then applied to the VIV simulations. Results from those simulations are compared and analyzed. The effects of two key soil properties on the VIV simulations of riser-conductor systems are then studied. Conclusions are made and suggestions are given for VIV analysis of riser-conductor systems and future researc

CFD Simulation of Vortex–Induced Vibrations of Free Span Pipelines Including Pipe-Soil Interactions

This paper presents a three dimensional numerical simulation of free span pipelines under vortex-induced vibrations (VIV) and pipe-soil interactions. Pipeline is simplified as a tensioned beam with uniformly distributed tension. The tensioned beam equations are solved using a fully implicit discretization scheme. The flow field around the pipeline is computed by numerically solving the unsteady Navier-Stokes equations. Fluid domain is discretized using overset grid system consists of several computational blocks and approximate one million grid points in total. Grid points in near-wall regions of pipeline and bottom are of high resolution, while far field flow is in relatively coarse grid. Fluid-structure interaction (FSI) is achieved by communicating forces and motions between fluid solver and pipeline motion solver. Pipeline motion solver inputs drag and lift forces calculated by fluid solver, then computes displacements in both in-line and cross-flow directions and outputs new positions of pipeline back to fluid solver. Soil effect also plays an important role in this simulation. The pipe-soil interactions are modeled as mass-spring system with equivalent stiffness. Simulation results are compared with experiments for validation in three cases: (a) An isolated pipeline VIV in uniform current without boundary effect; (b) A pipeline horizontally placed close to plane boundary in uniform current at different gap to diameter ratios G/D; (c) A free span pipeline at specific gap-to-diameter ratio with respect to different reduced velocities

Simulating water-entry/exit problems using Eulerian-Lagrangian and fully-Eulerian fictitious domain methods within the open-source IBAMR library

In this paper we employ two implementations of the fictitious domain (FD) method to simulate water-entry and water-exit problems and demonstrate their ability to simulate practical marine engineering problems. In FD methods, the fluid momentum equation is extended within the solid domain using an additional body force that constrains the structure velocity to be that of a rigid body. Using this formulation, a single set of equations is solved over the entire computational domain. The constraint force is calculated in two distinct ways: one using an Eulerian-Lagrangian framework of the immersed boundary (IB) method and another using a fully-Eulerian approach of the Brinkman penalization (BP) method. Both FSI strategies use the same multiphase flow algorithm that solves the discrete incompressible Navier-Stokes system in conservative form. A consistent transport scheme is employed to advect mass and momentum in the domain, which ensures numerical stability of high density ratio multiphase flows involved in practical marine engineering applications. Example cases of a free falling wedge (straight and inclined) and cylinder are simulated, and the numerical results are compared against benchmark cases in literature.Comment: The current paper builds on arXiv:1901.07892 and re-explains some parts of it for the reader's convenienc

Extension of the Overset Grid Preprocessor for Surface Conforming Meshes

RÉSUMÉ Un des défis à relever pour les aérodynamiciens numériciens est de développer des méthodes représentant le plus fidèlement possible la dynamique des fluides. L’augmentation des ressources de calcul disponibles permet maintenant à la dynamique des fluides numérique de représenter et résoudre adéquatement ces problèmes. Les travaux présentés dans ce mémoire se concentrent sur le développement d’une méthode pour résoudre les équations de Navier-Stokes sur des géométries complexes. Le logiciel utilisé pour faire ces simulations est celui développé à Polytechnique Montréal, NSCODE. Deux objectifs sont définis pour le projet: développer une méthode permettant la résolution de géométries complexes utilisant des maillages partageant une surface et démontrer la robustesse de la méthode en lien à des applications de type industriel. Dans le but d’augmenter les capacités de la méthode, une revue de littérature du développement de la méthode dans différents groupes de recherche, tels la NASA ou l’ONÉRA, a été faite. La méthode chimère, aussi connue sous son appellation anglaise «Overset», est choisie pour sa grande flexibilité à supporter des géométries complexes. Elle permet de mailler les différentes composantes d’une géométrie de façon indépendante entre celles-ci. Cela permet donc de simplifier la génération des maillages, étape complexe dans le processus de la dynamique des fluides numérique. La méthode chimère fait l’assemblage entre les différents maillages, utilisant des fonctions d’interpolation pour créer la communication entre eux. Une première version de la méthode avait précédemment été implémentée au sein du solveur NSCODE, mais n’avait été validée que sur des géométries dont les différentes composantes étaient entièrement entourées de fluide. Pour des géométries complexes, il n’est toutefois pas possible de procéder ainsi, et les maillages doivent pouvoir se superposer sur la surface de la géométrie. Trois axes de développement permettant d’élargir les capacités de la méthode actuelle sont identifiés. Premièrement, la méthode telle qu’implémentée présentait un algorithme de découpe de géométries (traduction libre du terme anglais «hole cutting») sommaire, échouant sur des géométries concaves. Un algorithme utilisant une triangulation Delaunay contrainte pour modéliser la géométrie est venu renforcir cette étape de la méthode chimère. Deuxièmement, pour supporter des maillages qui se superposent sur la même géométrie, l’interpolation dans les régions visqueuses a été étudiée. Principalement, les particularités liées au solveur, soit une discrétisation centrée aux cellules et un schéma de dissipation artificielle requérant 2 voisins, sont venues influencer les choix pour la méthode.----------ABSTRACT Aerodynamics engineers aspire to develop methods that represent with as much fidelity as possible fluid dynamics. With the fast growth of computational resources, Computational Fluid Dynamics (CFD) tools can now rely on high fidelity methods to solve these problems. This thesis focuses on the development of a method to solve the Navier-Stokes equations over complex geometries. The flow solver developed at Polytechnique Montreal, NSCODE, is the software used to perform the simulations. Two objectives are defined: develop a method to simulate complex geometries using surface conforming meshes and demonstrate its robustness with respect to industrial type applications. A literature review is conducted to evaluate the maturation of the overset method inside different research groups, notably the NASA and the ONERA. Also known as the Chimera method, it is selected based on its capacity to handle such difficult geometries. It allows to mesh different components individually, which ensures maximum grid quality. The mesh generation process is then simplified, which is regarded as a tedious and time consuming aspect of CFD. The overset method proceeds to perform the assembly of the different components together. Communication between these meshes is assured by using interpolation functions. An initial version of the overset method had previously been implemented inside NSCODE. Its validation was partially done, as it was only used for fully separated geometries. For complex geometries, this condition can not always be met, and the method must be able to treat meshes that overlap on the surface. Three development axis are identified to increase the capabilities of the current implementation. First, the hole cutting algorithm in place, while being a fast method, lacks of versatility towards more complex cases. Concave geometries lead to non valid grid assembly. An algorithm is developed to replace it, which uses a constrained Delaunay triangulation to represent accurately the internal geometry. Second, in order to support meshes with overlapping surfaces, a study of the interpolation in the viscous region is performed. Focus is given to the particularities of the flow solver, mainly the cell centred scheme as well as an artificial dissipation scheme, to influence the chosen methods. Two aspects are analyzed: the mesh generation for these meshes and the proper treatment of the boundary condition. A limitation is proposed to the mesh generation, to help ensure adequate grid assemblies and valid interpolation donors. Third, the manner to compute the aerodynamic forces and moments is addressed. A weighted panel method is introduced to avoid the double integration in overlapping regions

Direct numerical simulation of particulate flows with an overset grid method

We evaluate an efficient overset grid method for two-dimensional and three-dimensional particulate flows for small numbers of particles at finite Reynolds number. The rigid particles are discretised using moving overset grids overlaid on a Cartesian background grid. This allows for strongly-enforced boundary conditions and local grid refinement at particle surfaces, thereby accurately capturing the viscous boundary layer at modest computational cost. The incompressible Navier–Stokes equations are solved with a fractional-step scheme which is second-order-accurate in space and time, while the fluid–solid coupling is achieved with a partitioned approach including multiple sub-iterations to increase stability for light, rigid bodies. Through a series of benchmark studies we demonstrate the accuracy and efficiency of this approach compared to other boundary conformal and static grid methods in the literature. In particular, we find that fully resolving boundary layers at particle surfaces is crucial to obtain accurate solutions to many common test cases. With our approach we are able to compute accurate solutions using as little as one third the number of grid points as uniform grid computations in the literature. A detailed convergence study shows a 13-fold decrease in CPU time over a uniform grid test case whilst maintaining comparable solution accuracy.This work was supported by contracts from the U.S. Department of Energy ASCR Applied Math Program under grant AC52-07NA27344; the National Science Foundation under grant DMS-1519934; the Schlumberger Gould Research Centre under grant RG78221; the EPSRC Centre for Doctoral Training in Computational Methods for Materials Science under grant EP/L015552/1