Dimitrios Pavlidis

Anisotropic Mesh Adaptivity and Control Volume Finite Element Methods for Numerical Simulation of Multiphase Flow in Porous Media

Numerical simulation of multiphase flow in porous media is of great importance in a wide range of applications in science and engineering. The governing equations are the continuity equation and Darcy’s law. A novel control volume finite element (CVFE) approach is developed to discretize the governing equations in which a node-centered control volume approach is applied for the saturation equation, while a CVFE method is used for discretization of the pressure equation. We embed the discrete continuity equation into the pressure equation and ensure that the continuity equation is exactly enforced. Furthermore, the scheme is equipped with dynamic anisotropic mesh adaptivity which uses a metric tensor field approach, based on the curvature of fields of interest, to control the size and shape of elements in the metric space. This improves the resolution of the mesh in the zones of dynamic interest. Moreover, the mesh adaptivity algorithm employs multi-constraints on element size in different regions of the porous medium to resolve multi-scale transport phenomena. The advantages of mesh adaptivity and the capability of the scheme are demonstrated for simulation of flow in several challenging computational domains. The scheme captures the key features of flow while preserving the initial geometry and can be applied for efficient simulation of flow in heterogeneous porous media and geological formations.

Modelling of fluid–solid interactions using an adaptive mesh fluid model coupled with a combined finite–discrete element model

Fluid–structure interactions are modelled by coupling the finite element fluid/ocean model ‘Fluidity-ICOM’ with a combined finite–discrete element solid model ‘Y3D’. Because separate meshes are used for the fluids and solids, the present method is flexible in terms of discretisation schemes used for each material. Also, it can tackle multiple solids impacting on one another, without having ill-posed problems in the resolution of the fluid’s equations. Importantly, the proposed approach ensures that Newton’s third law is satisfied at the discrete level. This is done by first computing the action–reaction force on a supermesh, i.e. a function superspace of the fluid and solid meshes, and then projecting it to both meshes to use it as a source term in the fluid and solid equations. This paper demonstrates the properties of spatial conservation and accuracy of the method for a sphere immersed in a fluid, with prescribed fluid and solid velocities. While spatial conservation is shown to be independent of the mesh resolutions, accuracy requires fine resolutions in both fluid and solid meshes. It is further highlighted that unstructured meshes adapted to the solid concentration field reduce the numerical errors, in comparison with uniformly structured meshes with the same number of elements. The method is verified on flow past a falling sphere. Its potential for ocean applications is further shown through the simulation of vortex-induced vibrations of two cylinders and the flow past two flexible fibres.

Numerical simulation of three-dimensional breaking waves and its interaction with a vertical circular cylinder

Wave breaking plays an important role in wave-structure interaction. A novel control volume finite element method with adaptive unstructured meshes is employed here to study 3-D breaking waves. The numerical framework consists of a “volume of fluid” type method for the interface capturing and adaptive unstructured meshes to improve computational efficiency. The numerical model is validated against experimental measurements of breaking wave over a sloping beach and is then used to study the breaking wave impact on a vertical circular cylinder on a slope. Detailed complex interfacial structures during wave impact, such as plunging jet formation and splash-up are captured in the simulation, demonstrating the capability of the present method.

A New Approach to Reservoir Modeling and Simulation Using Boundary Representation, Adaptive Unstructured Meshes and the Discontinuous Overlapping Control Volume Finite Element Method

We present a new, high-order, control-volume-finite-element (CVFE) method with discontinuous Nth-order representation for pressure and (N 1)th-order for velocity. The method conserves mass and ensures that the extended Darcy equations for multi-phase flow are exactly enforced, but does not require the use of control volumes (CVs) that span domain boundaries. We demonstrate that the approach, amongst other features, accurately preserves sharp saturation changes associated with high aspect ratio geologic features such as fractures and mudstones, allowing efficient simulation of flow in highly heterogeneous models. Moreover, in conjunction with dynamic mesh optimization, in which the mesh adapts in space and time to key solution fields such as pressure, velocity or saturation whilst honoring a surface-based representation of the underlying geologic heterogeneity, accurate solutions are obtained at significantly lower computational cost than an equivalent fine, fixed mesh and conventional CVFE methods. The work presented is significant for two reasons. First, it resolves a long- standing problem associated with the use of classical CVFE methods to model flow in highly heterogeneous porous media; second, it reduces computational cost/increases solution accuracy through the use of dynamic mesh optimization without compromising parallelization.

THE IMMERSED BODY METHOD COMBINED WITH MESH ADAPTIVITY FOR FLUID-SOLID COUPLING

Modelling the interactions of fluids and solids is a challenge being actively pursued at most national laboratories and across engineering disciplines in many universities. Coastal and marine applications such as breakwater design, concrete armour unit stability, floating structures, ship motion, sedimentation, rock dumping and the growing field of energy conversion devices for wind, wave and tidal streams all have much to gain from an increased understanding through the modelling of such complex dynamics. Popular approaches include a Lagrangian Particle-FEM framework, space-time finite element techniques, lattice Boltzmann methods, smoothed particle hydrodynamics (SPH) and many variations of the immersed boundary method. The approach presented here is an immersed method with addition benefits of unstructured adaptive mesh optimisation and conservation of force. It models two-way coupled fluids-solids while harnessing accurate solid-solid interactions through use of the combined finite-discrete element method, FEMDEM. The potential exists for the deformability of the solids and therefore internal stresses to be captured in highly dynamic and energetic hydraulic environments.

Numerical Simulation of Air Flows in Street Canyons Using Mesh-Adaptive LES

In this study a novel approach for modelling urban atmospheric flows is presented. It uses a modified general purpose CFD model with anisotropic mesh adaptivity. The effect of traffic induced turbulence is modelled through a two-fluid approach giving the ability to explicitly model the movement of individual vehicles. Results are presented from the application of the model to a real urban area.