Mesh update techniques for free-surface flow solvers using spectral element method

This paper presents a novel mesh-update technique for unsteady free-surface Newtonian flows using spectral element method and relying on the arbitrary Lagrangian--Eulerian kinematic description for moving the grid. Selected results showing compatibility of this mesh-update technique with spectral element method are given

Three-dimensional CFD simulations with large displacement of the geometries using a connectivity-change moving mesh approach

This paper deals with three-dimensional (3D) numerical simulations involving 3D moving geometries with large displacements on unstructured meshes. Such simulations are of great value to industry, but remain very time-consuming. A robust moving mesh algorithm coupling an elasticity-like mesh deformation solution and mesh optimizations was proposed in previous works, which removes the need for global remeshing when performing large displacements. The optimizations, and in particular generalized edge/face swapping, preserve the initial quality of the mesh throughout the simulation. We propose to integrate an Arbitrary Lagrangian Eulerian compressible flow solver into this process to demonstrate its capabilities in a full CFD computation context. This solver relies on a local enforcement of the discrete geometric conservation law to preserve the order of accuracy of the time integration. The displacement of the geometries is either imposed, or driven by fluid–structure interaction (FSI). In the latter case, the six degrees of freedom approach for rigid bodies is considered. Finally, several 3D imposed-motion and FSI examples are given to validate the proposed approach, both in academic and industrial configurations

An Arbitrary-Lagrangian-Eulerian hybrid finite volume/finite element method on moving unstructured meshes for the Navier-Stokes equations

We present a novel second-order semi-implicit hybrid finite volume / finite element (FV/FE) scheme for the numerical solution of the incompressible and weakly compressible Navier-Stokes equations on moving unstructured meshes using an Arbitrary-Lagrangian-Eulerian (ALE) formulation. The scheme is based on a suitable splitting of the governing PDE into subsystems and employs staggered grids, where the pressure is defined on the primal simplex mesh, while the velocity and the remaining flow quantities are defined on an edge-based staggered dual mesh. The key idea of the scheme is to discretize the nonlinear convective and viscous terms using an explicit FV scheme that employs the space-time divergence form of the governing equations on moving space-time control volumes. For the convective terms, an ALE extension of the Ducros flux on moving meshes is introduced, which is kinetic energy preserving and stable in the energy norm when adding suitable numerical dissipation terms. Finally, the pressure equation of the Navier-Stokes system is solved on the new mesh configuration using a continuous FE method, with $\mathbb{P}_1$ Lagrange elements. The ALE hybrid FV/FE method is applied to several incompressible test problems ranging from non-hydrostatic free surface flows over a rising bubble to flows over an oscillating cylinder and an oscillating ellipse. Via the simulation of a circular explosion problem on a moving mesh, we show that the scheme applied to the weakly compressible Navier-Stokes equations is able to capture weak shock waves, rarefactions and moving contact discontinuities. We show that our method is particularly efficient for the simulation of weakly compressible flows in the low Mach number limit, compared to a fully explicit ALE schem

Thermodynamic Conditions in Quenching Chamber of Low Voltage Circuit Breaker

Práce se zabývá studiem procesů probíhajících při zhášení silnoproudého oblouku ve zhášecí komoře jističe. Je zaměřena na výpočet dynamiky tekutin a teplotního pole v okolí elektrického oblouku. V práci je dále popsán vliv vzdálenosti plechů v komoře a vliv tvarů plechů z hlediska aerodynamických podmínek uvnitř komory. Dalším cílem dosaženým touto prací je poskytnutí informací o vlivu polohy elektrického oblouku na termodynamické vlastnosti uvnitř komory. Toto je důležité, zejména pokud je oblouk do komory vtahován jinými silami, např. elektromagnetickými a během tohoto vtahovacího procesu mění svůj tvar i polohu. Za účelem co nejjednoduššího, ale zároveň co nejefektivnějšího řešení úkolu, byl vyvinut software určen speciálně pro výpočet dynamiky tekutin numerickou metodou konečných objemů (FVM). Tato metoda je, v porovnání s rozšířenější metodou konečných prvků (FEM), vhodnější pro výpočet dynamiky tekutin (CFD) zejména proto, že režie na výpočet jedné iterace jsou menší v porovnání s ostatními numerickými metodami. Další výhodou tohoto softwarového řešení je jeho modularita a rozšiřitelnost. Cely koncept softwaru je postaven na tzv. zásuvných modulech. Díky tomuto řešení můžeme využít výpočtové jádro pro další numerické analýzy, např. strukturální, elektromagnetickou apod. Jediná potřeba pro úspěšné používání těchto analýz je napsáni solveru pro konečné prvky (FEM). Jelikož je software koncipován jako multi–thread aplikace, využívá výkon současných vícejádrových procesorů naplno. Tato vlastnost se ještě více projeví, pokud se výpočet přesune z CPU na GPU. Jelikož současné grafické karty vyšších tříd mají několik desítek až stovek výpočetních jader a pracují s mnohem rychlejšími pamětmi, než CPU, je výpočetní výkon několikanásobně vyšší.Work deals with the study of processes that attend the electric arc extinction inside the quenching chamber of a circuit breaker. It is focused on several areas. The first one is concerned to fluid dynamics calculations (CFD) and the second one is aimed at thermal field calculations. In this work effects of metal plates distance together with metal plates shapes are described from aerodynamical point of view. Another objective solved by this work is to give information about influence of an electric arc position in a quenching chamber, which changed its shape due to forces acting on it during extinction process. For purpose of this work a new software solution for CFD was developed. Whole software concept is based on plug-ins. Due to this solution, the software§s calculation core can be used for other numerical analyses, like structural, electromagnetic, etc. The only requirement is to write a plug-in for these analyses. Because the software is designed as multi-threaded application, it can use the fully performance of current multi-core processors. Above mentioned property can be especially shown off, when a calculation is moved from CPU to GPU (Graphics Processing Units). Current high-end graphic cards have tens to hundreds cores and work with faster memories than CPU. Due to this fact, the simulation performance can raised manifold.

Interface Tracking and Solid-Fluid Coupling Techniques with Coastal Engineering Applications

Multi-material physics arise in an innumerable amount of engineering problems. A broadly scoped numerical model is developed and described in this thesis to simulate the dynamic interaction of multi-fluid and solid systems. It is particularly aimed at modelling the interaction of two immiscible fluids with solid structures in a coastal engineering context; however it can be extended to other similar areas of research. The Navier Stokes equations governing the fluids are solved using a combination of finite element (FEM) and control volume finite element (CVFE) discretisations. The sharp interface between the fluids is obtained through the compressive transport of material properties (e.g. material concentration). This behaviour is achieved through the CVFE method and a conveniently limited flux calculation scheme based on the Hyper-C method by Leonard (1991). Analytical and validation test cases are provided, consisting of steady and unsteady flows. To further enhance the method, improve accuracy, and exploit Lagrangian benefits, a novel moving mesh method is also introduced and tested. It is essentially an Arbitrary Lagrangian Eulerian method in which the grid velocity is defined by semi-explicitly solving an iterative functional minimisation problem. A multi-phase approach is used to introduce solid structure modelling. In this approach, solution of the velocity field for the fluid phase is obtained using Model B as explained by Gidaspow (1994, page 151). Interaction between the fluid phase and the solids is achieved through the means of a source term included in the fluid momentum equations. The interacting force is calculated through integration of this source term and adding a buoyancy contribution. The resulting force is passed to an external solid-dynamics model such as the Discrete Element Method (DEM), or the combined Finite Discrete Element Method (FEMDEM). The versatility and novelty of this combined modelling approach stems from its ability to capture the fluid interaction with particles of random size and shape. Each of the three main components of this thesis: the advection scheme, the moving mesh method, and the solid interaction are individually validated, and examples of randomly shaped and sized particles are shown. To conclude the work, the methods are combined together in the context of coastal engineering applications, where the complex coupled problem of waves impacting on breakwater amour units is chosen to demonstrate the simulation possibilities. The three components developed in this thesis significantly extend the application range of already powerful tools, such as Fluidity, for fluids-modelling and finite discrete element solids-modelling tools by bringing them together for the first time

A Provably Stable Discontinuous Galerkin Spectral Element Approximation for Moving Hexahedral Meshes

We design a novel provably stable discontinuous Galerkin spectral element (DGSEM) approximation to solve systems of conservation laws on moving domains. To incorporate the motion of the domain, we use an arbitrary Lagrangian-Eulerian formulation to map the governing equations to a fixed reference domain. The approximation is made stable by a discretization of a skew-symmetric formulation of the problem. We prove that the discrete approximation is stable, conservative and, for constant coefficient problems, maintains the free-stream preservation property. We also provide details on how to add the new skew-symmetric ALE approximation to an existing discontinuous Galerkin spectral element code. Lastly, we provide numerical support of the theoretical results