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Showing 1 to 20 of 41 for “"finite volume methods"”.
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Computational stress analysis using finite volume methods
There is a growing interest in applying finite volume methods to model solid mechanics problems and multi-physics phenomena. During the last ten years an increasing amount of activity has taken place in this area. Unlike the finite element formulation, which generally involves volume integrals, the …
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Geometry-based finite volume methods for modelling transport on micro-CT images
… flow mechanisms. In this Thesis, a Pore-scale Finite Volume Solver (PFVS) is proposed that solves an elliptic diffusion equation to obtain the spatial pressure distribution on the entire micro-CT image. The flow results have 11% error compared to other solvers such as Stokes solver and …
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DEVELOPMENT OF HIGH-ORDER FINITE VOLUME METHODS ON UNSTRUCTURED GRIDS AND THEIR APPLICATIONS
… bottleneck problems of the existing high-order methods, two straightforward mesh-free scheme-based high-order finite volume (FV) methods on unstructured grids are developed in this thesis for simulation of various flow problems. Under the basic framework of the unstructured finite volume method, …
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Structure-preserving finite element and finite volume methods for nonlinear and time-dependent PDEs
… conclude by addressing the question of whether finite element methods satisfy a discrete multisymplectic conservation law. We find that all analyzed methods satisfy a strong version of this property, except the Arnold-FalkWinther conforming method, which satisfies the multisymplectic property …
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A study of well-balanced finite volume methods and refinement indicators for the shallow water equations
… parts. The first part is about well-balanced finite volume methods to solve steady and unsteady state problems. A method is said to be well-balanced if it preserves an unperturbed steady state at the discrete level. We implement hydrostatic reconstructions for the well-balanced methods with …
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A study of well-balanced finite volume methods and refinement indicators for the shallow water equations
… parts. The first part is about well-balanced finite volume methods to solve steady and unsteady state problems. A method is said to be well-balanced if it preserves an unperturbed steady state at the discrete level. We implement hydrostatic reconstructions for the well-balanced methods with …
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Simulation of blood flows in a stenosed and bifurcating artery using finite volume methods and OpenFOAM
… the OldroydB, Giesekus, Johnson-Segalman, Finitely Extensible Non-Linear Elastic (FENE), Phan-Thein-Tanner (PTT) models etc. Our Numerical approach is based on the finite volume methods implemented on the OpenFOAM platform. We employ the Giesekus, Oldroyd-B, and Generalized Oldroyd-B …
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Discretization Error Estimation Using the Error Transport Equations for Computational Fluid Dynamics Simulations
… Typical spatial discretization schemes include finite-difference methods, finite-volume methods, and finite-element methods. Error introduced in the discretization process is called discretization error and defined as the difference between the exact solution to the discrete equations and the …
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Covolume-Upwind Finite Volume Approximations For Linear Elliptic Partial Differential Equations
<p>In this dissertation we study covolume-upwind finite volume methods on rectilinear grids for solving second-order linear elliptic partial differential equations with mixed boundary conditions. This class of problems has intensive applications in various fields of science and engineering, e.g., …
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STRUCTURE-OPTIMIZED AND ORDER-PRESERVING METHODS FOR ADVECTION AND TIME STEPPING
… fundamental shortcomings in computational methods for differential equations by developing novel high-order accurate numerical schemes that can apply to multi-physics or multi-scale problems. Motivated by the need for numerical methods with long-time accurate solutions in complex …
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Fully coupled CEM/CFD modelling of microwave heating in a porous medium
… material are presented in this paper. Coupled finite difference time domain and finite volume methods are used to solve equations that describe the electromagnetic field and heat and mass transfer in porous media. These equations are nonlinearly coupled through the dielectric properties which …
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Domain Decomposition Methods for Convection-Diffusion-Reaction Equations with Finite Volume Discretizations
… (CDR) model with the finite volume discretization are studied. Both overlapping and non-overlapping domain decom- position (DD) preconditioning methods are considered. With overlapping DD preconditioners, we work on a time dependent CDR model. The additive Runge-Kutta …
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Finite volume modelling of low speed structural impact problems
… in this thesis on the common theme of applying finite volume methods to simulate structural impact problems. The first investigation is the application of the Eulerian Finite Volume Method (EFVM) to simulate the low-speed impact of ductile materials. Simulation results are validated against …
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Modelling and computational analysis of heat-transfer in multi-geometry and multi-phase flow of Newtonian and non-Newtonian fluids in pipes and channels
… algorithms for these problems are based on the Finite Volume Methods (FVM) implemented on the OpenFOAM software. The numerical instabilities due to the High Weissenburg Number Problem (HWNP) are resolved by employing either the Discrete Elastic Viscous Stress Splitting (DEVSS) or the Log …
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Computational analysis of non-isothermal flow of non-Newtonian fluids
… on geometrical or mathematical complexity, finite difference or finite volume methods will be adopted. We present the results from our numerical simulations via graphical illustrations and validate them (qualitatively) against' similar' results in the literature; the quotes being necessary …
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Development of a flow-condition-based interpolation 9-node element for incompressible flows
… to certain values, oscillations appear in the finite element solution of the Navier-Stokes equations. In order to solve for high Reynolds number flows and avoid the oscillations, one technique is to use the flow condition-based interpolation scheme (FCBI), which is a hybrid of the finite …
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Acceleration of Eulerian Multi-Material Methods on Highly Parallel Compute Architectures
… for numerical schemes commonly used in finite-volume methods, the solution of the Eikonal equation in a narrow band, the Ghost Fluid Method (GFM), and signed-distance function generation from multiple external geometry file types. Additionally, we present the main problems involved in …
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Experimental Investigation of Shock-Shock Interactions over a 2-D Wedge at M = 6
… data were analyzed using one-dimensional semi-infinite as well as one- and two-dimensional finite-volume methods to determine the proper heat transfer analysis approach to minimize errors from lateral heat conduction due to the presence of strong surface temperature gradients induced by the shock …
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