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Finite Volume Formulation (finite + volume_formulation)
Selected AbstractsA domain decomposition approach to finite volume solutions of the Euler equations on unstructured triangular meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2001Victoria Dolean Abstract We report on our recent efforts on the formulation and the evaluation of a domain decomposition algorithm for the parallel solution of two-dimensional compressible inviscid flows. The starting point is a flow solver for the Euler equations, which is based on a mixed finite element/finite volume formulation on unstructured triangular meshes. Time integration of the resulting semi-discrete equations is obtained using a linearized backward Euler implicit scheme. As a result, each pseudo-time step requires the solution of a sparse linear system for the flow variables. In this study, a non-overlapping domain decomposition algorithm is used for advancing the solution at each implicit time step. First, we formulate an additive Schwarz algorithm using appropriate matching conditions at the subdomain interfaces. In accordance with the hyperbolic nature of the Euler equations, these transmission conditions are Dirichlet conditions for the characteristic variables corresponding to incoming waves. Then, we introduce interface operators that allow us to express the domain decomposition algorithm as a Richardson-type iteration on the interface unknowns. Algebraically speaking, the Schwarz algorithm is equivalent to a Jacobi iteration applied to a linear system whose matrix has a block structure. A substructuring technique can be applied to this matrix in order to obtain a fully implicit scheme in terms of interface unknowns. In our approach, the interface unknowns are numerical (normal) fluxes. Copyright © 2001 John Wiley & Sons, Ltd. [source] Interface tracking finite volume method for complex solid,fluid interactions on fixed meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2002H. S. Udaykumar Abstract We present a numerical technique for computing flowfields around moving solid boundaries immersed in fixed meshes. The mixed Eulerian,Lagrangian framework treats the immersed boundaries as sharp solid,fluid interfaces and a conservative finite volume formulation allows boundary conditions at the moving surfaces to be exactly applied. A semi-implicit second-order accurate spatial and temporal discretization is employed with a fractional-step scheme for solving the flow equations. A multigrid accelerator for the pressure Poisson equations has been developed to apply in the presence of multiple embedded solid regions on the mesh. We present applications of the method to two types of problems: (a) solidification in the presence of flows and particles, (b) fluid,structure interactions in flow control. In both these problems, the sharp interface method presents advantages by being able to track arbitrary interface motions, while capturing the full viscous, unsteady dynamics. Copyright © 2001 John Wiley & Sons, Ltd. [source] A finite volume method for large strain analysis of incompressible hyperelastic materialsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2005I. Bijelonja Abstract This paper describes development of a displacement,pressure based finite volume formulation for modelling of large strain problems involving incompressible hyperelastic materials. The method is based on the solution of the integral conservation equations governing momentum balance in total Lagrangian description. The incompressibility constraint is enforced by employing the integral form of the mass conservation equation in deformed configurations of the body. A Mooney,Rivlin incompressible material model is used for material description. A collocated variable arrangement is used and the spatial domain is discretized using finite volumes of an arbitrary polyhedral shape. A segregated approach is employed to solve resulting set of coupled non-linear algebraic equations, utilizing a SIMPLE based algorithm for displacement,pressure coupling. Comparisons of numerical and analytical results show a very good agreement. For the limited range of cell topologies tested the developed method appears to be locking free. Copyright © 2005 John Wiley & Sons, Ltd. [source] Some results on the accuracy of an edge-based finite volume formulation for the solution of elliptic problems in non-homogeneous and non-isotropic mediaINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2009Darlan Karlo Elisiário de Carvalho Abstract The numerical simulation of elliptic type problems in strongly heterogeneous and anisotropic media represents a great challenge from mathematical and numerical point of views. The simulation of flows in non-homogeneous and non-isotropic porous media with full tensor diffusion coefficients, which is a common situation associated with the miscible displacement of contaminants in aquifers and the immiscible and incompressible two-phase flow of oil and water in petroleum reservoirs, involves the numerical solution of an elliptic type equation in which the diffusion coefficient can be discontinuous, varying orders of magnitude within short distances. In the present work, we present a vertex-centered edge-based finite volume method (EBFV) with median dual control volumes built over a primal mesh. This formulation is capable of handling the heterogeneous and anisotropic media using structured or unstructured, triangular or quadrilateral meshes. In the EBFV method, the discretization of the diffusion term is performed using a node-centered discretization implemented in two loops over the edges of the primary mesh. This formulation guarantees local conservation for problems with discontinuous coefficients, keeping second-order accuracy for smooth solutions on general triangular and orthogonal quadrilateral meshes. In order to show the convergence behavior of the proposed EBFV procedure, we solve three benchmark problems including full tensor, material heterogeneity and distributed source terms. For these three examples, numerical results compare favorably with others found in literature. A fourth problem, with highly non-smooth solution, has been included showing that the EBFV needs further improvement to formally guarantee monotonic solutions in such cases. Copyright © 2008 John Wiley & Sons, Ltd. [source] A Taylor series-based finite volume method for the Navier,Stokes equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2008G. X. Wu Abstract A Taylor series-based finite volume formulation has been developed to solve the Navier,Stokes equations. Within each cell, velocity and pressure are obtained from the Taylor expansion at its centre. The derivatives in the expansion are found by applying the Gauss theorem over the cell. The resultant integration over the faces of the cell is calculated from the value at the middle point of the face and its derivatives, which are further obtained from a higher order interpolation based on the values at the centres of two cells sharing this face. The terms up to second order in the velocity and the terms up to first order in pressure in the Taylor expansion are retained throughout the derivation. The test cases for channel flow, flow past a circular cylinder and flow in a collapsible channel have shown that the method is quite accurate and flexible. Copyright © 2008 John Wiley & Sons, Ltd. [source] Level-set based numerical simulation of a migrating and dissolving liquid drop in a cylindrical cavityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2004Edmondo Bassano Abstract In the present paper the dissolution of a binary liquid drop having a miscibility gap and migrating due to thermo-solutal capillary convection in a cylindrical cavity is studied numerically. The interest in studying this problem is twofold. From a side, in the absence of gravity, capillary migration is one of the main physical mechanisms to set into motion dispersed liquid phases and from the other side, phase equilibria of multi-component liquid systems, ubiquitous in applications, often exhibit a miscibility gap. The drop capillary migration is due to an imposed temperature gradient between the cavity top and bottom walls. The drop dissolution is due to the fact that initial composition and volume values, and thermal boundary conditions are only compatible with a final single phase equilibrium state. In order to study the drop migration along the cavity and the coupling with dissolution, a previously developed planar two-dimensional code is extended to treat axis-symmetric geometries. The code is based on a finite volume formulation. A level-set technique is used for describing the dynamics of the interface separating the different phases and for mollifying the interface discontinuities between them. The level-set related tools of redistancing and off-interface extension are used to enhance code resolution in the critical interface region. Migration speeds and volume variations are determined for different drop radii. Copyright © 2004 John Wiley & Sons, Ltd. [source] | ||||||||||