A development of high resolution NFT model for simulation of incompressible flows is presented. The model uses finite volume spatial discretisation with edge based data structure and operates on unstructured meshes with arbitrary shaped cells. The key features of the model include non-oscillatory advection scheme Multidimensional Positive Definite Advection Transport Algorithm (MPDATA) and non-symmetric Krylov-subspace elliptic solver. The NFT MPDATA model integrates the Reynolds Average Navier Stokes (RANS) equations. The implementation of the Spalart-Allmaras one equations turbulence model extends the development further to turbulent flows. An efficient non-staggered mesh arrangement for pressure and velocity is employed and provides smooth solutions without a need of artificial dissipation. In contrast to commonly used schemes, a collocated arrangement for flow variables is possible as the stabilisation of the NFT MPDATA scheme arises naturally from the design of MPDATA. Other benefits of MPDATA include: second order accuracy, strict sign-preserving and full multidimensionality. The flexibility and robustness of the new approach is studied and validated for laminar and turbulent flows. Theoretical developments are supported by numerical testing. Successful quantitative and qualitative comparisons with the numerical and experimental results available from literature confirm the validity and accuracy of the NFT MPDATA scheme and open the avenue for its exploitation for engineering problems with complex geometries requiring flexible representation using unstructured meshes.

This work is part of an effort to develop an unstructured, three-dimensional, direct simulation Monte Carlo/particle-in-cell (DSMC/PIC) code for the simulation of non-ionized, fully ionized and partially-ionized flows in micropropulsion devices. Flows in microthrusters are often in the transitional to rarefied regimes, requiring numerical techniques based on the kinetic description of the gaseous or plasma propellants. The code is implemented on unstructured tetrahedral grids to allow discretization of arbitrary surface geometries and includes an adaptation capability. In this study, an existing 3D DSMC code for rarefied gasdynamics is improved with the addition of the variable hard sphere model for elastic collisions and a vibrational relaxation model based on discrete harmonic oscillators. In addition the existing unstructured grid generation module of the code is enhanced with grid-quality algorithms. The unstructured DSMC code is validated with simulation of several gaseous micronozzles and comparisons with previous experimental and numerical results. Rothe s 5-mm diameter micronozzle operating at 80 Pa is simulated and results are compared favorably with the experiments. The Gravity Probe-B micronozzle is simulated in a domain that includes the injection chamber and plume region. Stagnation conditions include a pressure of 7 Pa and mass flow rate of 0.012 mg/s. The simulation examines the role of injection conditions in micronozzle simulations and results are compared with previous Monte Carlo simulations. The code is also applied to the simulation of a parabolic planar micronozzle with a 15.4-micron throat and results are compared with previous 2D Monte Carlo simulations. Finally, the code is applied to the simulation of a 34-micron throat MEMS-fabricated micronozzle. The micronozzle is planar in profile with sidewalls binding the upper and lower surfaces. The stagnation pressure is set at 3.447 kPa and represents an order of magnitude lower pressure than used in previous experiments. The simulation demonstrates the formation of large viscous boundary layers in the sidewalls. A particle-in-cell model for the simulation of electrostatic plasmas is added to the DSMC code. Solution to Poisson's equation on unstructured grids is obtained with a finite volume implementation. The Poisson solver is validated by comparing results with analytic solutions. The integration of the ionized particle equations of motion is performed via the leapfrog method. Particle gather and scatter operations use volume weighting with linear Lagrange polynomial to obtain an acceptable level of accuracy. Several methods are investigated and implemented to calculate the electric field on unstructured meshes. Boundary conditions are discussed and include a formulation of plasma in bounded domains with external circuits. The unstructured PIC code is validated with the simulation of a high voltage sheath formation.

The intrinsic flexibility of unstructured meshes is compelling for numerical ocean modeling. Complex topographic features, such as coastlines, islands and narrow straits, can faithfully be represented by locally increasing the mesh resolution and because there is no constraint on the mesh topology. In that respect, the finite element method is particularly promising. Not only does it allow for naturally handling unstructured meshes but it also offers additional flexibility in the choice of interpolation and is sustained by a rich and rigorous mathematical framework. This doctoral research was carried out under the auspices of the SLIM (Second-generation Louvain-la-Neuve Ice-ocean Model) project, the objective of which is to develop an ocean general circulation model using the finite element method. This PhD dissertation deals with one-, two- and three-dimensional finite element ocean modeling. We chiefly focus on the accurate representation of some selected oceanic processes and we devote much effort toward using a consistent finite element method to solve the underlying equations. We first concentrate on the finite element solution to a one-dimensional benchmark for the propagation of Poincaré waves with particular emphasis on the discontinuous Galerkin method and a physical justification for computing the numerical fluxes. We then compare three finite element formulations (vorticity - streamfunction, velocity - pressure and free-surface) for the solution to geophysical fluid flow instabilities problems. The prominent -- and remaining -- part of this work deals with three-dimensional ocean modeling on moving meshes. It covers the selection of the right elements for the vertical velocity and tracers through achieving strict tracer conservation and local consistency between the elevation, continuity and tracer equations. The ensuing three-dimensional model is successfully validated against a realistic tidal flow around a shallow-water island. New physical insights are proposed as to the physical processes encountered in such flows.

The reaction-diffusion master equation (RDME) is a stochastic model for spatially heterogeneous chemical systems. Stochastic models have proved to be useful for problems from molecular biology since copy numbers of participating chemical species often are small, which gives a stochastic behaviour. The RDME is a discrete space model, in contrast to spatially continuous models based on Brownian motion. In this thesis two accuracy issues of the RDME on unstructured meshes are studied. The first concerns the rates of diffusion events. Errors due to previously used rates are evaluated, and a second order accurate finite volume method, not previously used in this context, is implemented. The new discretisation improves the accuracy considerably, but unfortunately it puts constraints on the mesh, limiting its current usability. The second issue concerns the rates of bimolecular reactions. Using the macroscopic reaction coefficients these rates become too low when the spatial resolution is high. Recently, two methods to overcome this problem by calculating mesoscopic reaction rates for Cartesian meshes have been proposed. The methods are compared and evaluated, and are found to work remarkably well. Their possible extension to unstructured meshes is discussed.

Plasma-assisted processing and deposition of materials is an important component of modern industrial applications, with plasma reactors sharing 30% to 40% of manufacturing steps in microelectronics production [1]. Development of new flexible electronics increases demands for efficient high-throughput deposition methods and roll-to-roll processing of materials. The current work represents an attempt of practical design and numerical modeling of a plasma enhanced chemical vapor deposition system. The system utilizes plasma at standard pressure and temperature to activate a chemical precursor for protective coatings. A specially designed linear plasma head, that consists of two parallel plates with electrodes placed in the parallel arrangement, is used to resolve clogging issues of currently available commercial plasma heads, as well as to increase the flow-rate of the processed chemicals and to enhance the uniformity of the deposition. A test system is build and discussed in this work. In order to improve operating conditions of the setup and quality of the deposited material, we perform numerical modeling of the plasma system. The theoretical and numerical models presented in this work comprehensively describe plasma generation, recombination, and advection in a channel of arbitrary geometry. Number density of plasma species, their energy content, electric field, and rate parameters are accurately calculated and analyzed in this work. Some interesting engineering outcomes are discussed with a connection to the proposed setup. The numerical model is implemented with the help of high-performance parallel technique and evaluated at a cluster for parallel calculations. A typical performance increase, calculation speed-up, parallel fraction of the code and overall efficiency of the parallel implementation are discussed in details.

Visualization of large amounts of simulation data is important for the understanding of most physical phenomena. The limited capabilities of desktop machines make them unsuitable for handling excessive amounts of simulation data. The present day high speed networks have made it possible to remotely visualize the data being generated by a supercomputer in real time. In order for such a system to be reliable, a robust communication protocol and an efficient compression mechanism are needed. This work presents a remote visualization system that addresses these issues, and emphasizes the design and implementation of the application level network protocol. A control theory based adaptive rate control algorithm is presented for UDP streams that maximizes the effective throughout experienced by the stream while minimizing the packet loss. The algorithm is shown to make the system responsive to changing network conditions. This makes the system deployable over any network, including the Internet. / Master of Science

A Large Eddy-Simulation code, based on a mesh transparent algorithm, for hybrid unstructured meshes is presented to deal with complex geometries that are often found in engineering flow problems. While tetrahedral elements are very effective in dealing with complex geometry, excessive numerical diffusion often affects results. Thus, prismatic or hexahedral elements are preferable in regions where turbulence structures are important. A second order reconstruction methodology is used since an investigation of a higher order method based upon Lele's compact scheme has shown this to be impractical on general unstructured meshes. The convective fluxes are treated with the Roe scheme that has been modified by introducing a variable scaling to the dissipation matrix to obtain a nearly second order accurate centred scheme in statistically smooth flow, whilst retaining the high resolution TVD behaviour across a shock discontinuity. The code has been parallelised using MPI to ensure portability. The base numerical scheme has been validated for steady flow computations over complex geometries using inviscid and RANS forms of the governing equations. The extension of the numerical scheme to unsteady turbulent flows and the complete LES code have been validated for the interaction of a shock with a laminar mixing layer, a Mach 0.9 turbulent round jet and a fully developed turbulent pipe flow. The mixing layer and round jet computations indicate that, for similar mesh resolution of the shear layer, the present code exhibits results comparable to previously published work using a higher order scheme on a structured mesh. The unstructured meshes have a significantly smaller total number of nodes since tetrahedral elements are used to fill to the far field region. The pipe flow results show that the present code is capable of producing the correct flow features. Finally, the code has been applied to the LES computation of the impingement of a highly under-expanded jet that produces plate shock oscillation. Comparison with other workers' experiments indicates good qualitative agreement for the major features of the flow. However, in this preliminary computation the computed frequency is somewhat lower than that of experimental measurements.

In this thesis we develop 2D parallel unstructured mesh adaptation methods for the solution of partial differential equations (PDEs) by the finite element method (FEM). Additionally, we develop a novel block preconditioner for the iterative solution of the linear systems arising from the finite element discretisation of the Föppl-von Kàrmàn equations. Two of the problems arising in the numerical solution of PDEs by FEM are the memory constraints that limit the solution of large problems, and the inefficiency of solving the associated linear systems by direct or iterative solvers. We initially focus on mesh adaptation, which is a memory demanding task of the FEM. The size of the problem increases by adding more elements and nodes to the mesh during mesh refinement. In problems involving a large number of elements, the problem size is limited by the memory available on a single processor. In order to be able to work with large problems, we use a domain decomposition approach to distribute the problem over multiple processors. One of the main objectives of this thesis is the development of 2D parallel unstructured mesh adaptation methods for the solution of PDEs by the FEM in a variety of problems; including domains with curved boundaries, holes and internal boundaries. Our newly developed methods are implemented in the software library oomph-lib, an open-source object oriented multi-physics software library implementing the FEM. We validate and demonstrate their utility in a set of increasingly complex problems ranging from scalar PDEs to fully coupled multi-physics problems. Having implemented and validated the infrastructure which facilitates the finite-element-based discretisation of PDEs in a distributed environment, we shift our focus to the second problem concerning this thesis and one of the major challenges in the computational solution of PDEs: the solution of the large linear systems arising from their discretisation. For sufficiently large problems, the solution of their associated linear system by direct solvers becomes impossible or inefficient, typically because of memory and time constraints. We therefore focus on preconditioned Krylov subspace methods whose efficiency depends crucially on the provision of a good preconditioner. These preconditioners are invariably problem dependent. We illustrate their application and development in the solution of two elasticity problems which give rise to relatively large problems. First we consider the solution of a linear elasticity problem and compute the stress distribution near a crack tip where strong local mesh refinement is required. We then consider the deformation of thin plates which are described by the nonlinear Föppl-von Kàrmàn equations. A key contribution of this work is the development of a novel block preconditioner for the iterative solution of these equations, we present the development of the preconditioner and demonstrate its practical performance.

Cette thèse pose les fondations du modèle « the Second-generation Louvain-la-Neuve Ice-ocean Model » (SLIM) qui est basé sur la méthode des éléments finis et les maillages non-structurés. Ce modèle fait partie d'une seconde génération de modèles numériques de circulation marine ou océanique. Notre travail a principalement porté sur les aspects géométriques liés à l'utilisation des maillages non-structurés. Nous avons implémenté un algorithme de triangulation qui génère automatiquement des maillages anisotropes non-structurés sur le plan et la sphère et nous avons défini des stratégies de raffinement de maillage adaptées aux applications marines. Ces stratégies orchestrent la distribution de la taille et de la forme des éléments du maillage afin d'optimiser la précision et le coût en temps de calcul du nouveau modèle. Nous avons aussi abordé l'interpolation contrainte de champs scalaires et vectoriels d'un premier maillage vers un second. L'utilisation conjointe de ces trois outils combinée avec un estimateur d'erreur a posteriori permettra l'adaptation dynamique de maillages au cours de simulations transitoires. Finalement, nous avons bâti les outils géométriques nécessaires à l'écriture d'une formulation discrète des équations de la dynamique des fluides géophysiques sur la sphère. Basée sur un système de coordonnées curvilignes propre à chaque élément du maillage, cette approche originale ne possède aucune des difficultés mathématiques et numériques liées aux singularités des pôles et auxquelles les modèles de la première génération n'ont pu apporter de solution entièrement satisfaisante.

Cette thèse pose les fondations du modèle « the Second-generation Louvain-la-Neuve Ice-ocean Model » (SLIM) qui est basé sur la méthode des éléments finis et les maillages non-structurés. Ce modèle fait partie d'une seconde génération de modèles numériques de circulation marine ou océanique. Notre travail a principalement porté sur les aspects géométriques liés à l'utilisation des maillages non-structurés. Nous avons implémenté un algorithme de triangulation qui génère automatiquement des maillages anisotropes non-structurés sur le plan et la sphère et nous avons défini des stratégies de raffinement de maillage adaptées aux applications marines. Ces stratégies orchestrent la distribution de la taille et de la forme des éléments du maillage afin d'optimiser la précision et le coût en temps de calcul du nouveau modèle. Nous avons aussi abordé l'interpolation contrainte de champs scalaires et vectoriels d'un premier maillage vers un second. L'utilisation conjointe de ces trois outils combinée avec un estimateur d'erreur a posteriori permettra l'adaptation dynamique de maillages au cours de simulations transitoires. Finalement, nous avons bâti les outils géométriques nécessaires à l'écriture d'une formulation discrète des équations de la dynamique des fluides géophysiques sur la sphère. Basée sur un système de coordonnées curvilignes propre à chaque élément du maillage, cette approche originale ne possède aucune des difficultés mathématiques et numériques liées aux singularités des pôles et auxquelles les modèles de la première génération n'ont pu apporter de solution entièrement satisfaisante.