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Finite-volume lattice Boltzmann method
Physical Review E, 1999We present a finite-volume formulation for the lattice Boltzmann method (FVLBM) based on standard bilinear quadrilateral elements in two dimensions. The accuracy of this scheme is demonstrated by comparing the velocity field with the analytical solution of the Navier-Stokes equations for time dependent rotating Couette flow and Taylor vortex flow.
H, Xi, G, Peng, S H, Chou
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1996
As in the previous chapter, we shall consider only the generic conservation equation for a quantity φ and assume that the velocity field and all fluid properties are known. The finite volume method uses the integral form of the conservation equation as the starting point: $$\int_S \rho\phi\upsilon\,\cdot n\,{\text{d}}S = \int_S \Gamma\,{\text{grad}}
Joel H. Ferziger, Milovan Perić
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As in the previous chapter, we shall consider only the generic conservation equation for a quantity φ and assume that the velocity field and all fluid properties are known. The finite volume method uses the integral form of the conservation equation as the starting point: $$\int_S \rho\phi\upsilon\,\cdot n\,{\text{d}}S = \int_S \Gamma\,{\text{grad}}
Joel H. Ferziger, Milovan Perić
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2018
One major difference between the finite difference method (FDM) and the finite volume method (FVM) is that the FVM is based on the integral form of the governing equations instead of the differential form. In the FVM, this discretization is conducted over each control volume, which endows FVM with advantages of mass conservation and unstructured meshes.
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One major difference between the finite difference method (FDM) and the finite volume method (FVM) is that the FVM is based on the integral form of the governing equations instead of the differential form. In the FVM, this discretization is conducted over each control volume, which endows FVM with advantages of mass conservation and unstructured meshes.
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2002
The Finite Volume Method (FVM) was introduced into the field of computational fluid dynamics in the beginning of the seventies (McDonald 1971, Mac-Cormack and Paullay 1972). From the physical point of view the FVM is based on balancing fluxes through control volumes, i. e. the Eulerian concept is used (see section 1.1.4).
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The Finite Volume Method (FVM) was introduced into the field of computational fluid dynamics in the beginning of the seventies (McDonald 1971, Mac-Cormack and Paullay 1972). From the physical point of view the FVM is based on balancing fluxes through control volumes, i. e. the Eulerian concept is used (see section 1.1.4).
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International Journal for Numerical Methods in Engineering, 1999
A new finite volume method for elliptic problems is presented and analyzed. The method employs a mixed primal-dual formulation in which two dual meshes are used. Error estimates are developed and numerical results are presented.
Thomas, J.-M., Trujillo, D.
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A new finite volume method for elliptic problems is presented and analyzed. The method employs a mixed primal-dual formulation in which two dual meshes are used. Error estimates are developed and numerical results are presented.
Thomas, J.-M., Trujillo, D.
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1999
As demonstrated in the preceding chapters, the errors in most numerical solutions increase dramatically as the physical scale of the simulated disturbance approaches the minimum scale resolvable on the numerical mesh. When solving equations for which smooth initial data guarantees a smooth solution at all later times, such as the barotropic vorticity ...
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As demonstrated in the preceding chapters, the errors in most numerical solutions increase dramatically as the physical scale of the simulated disturbance approaches the minimum scale resolvable on the numerical mesh. When solving equations for which smooth initial data guarantees a smooth solution at all later times, such as the barotropic vorticity ...
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2012
Beside the finite difference and finite element methods, a new numerical method has been recently proposed, which looks to be very promising for stable and reliable solutions of the fundamental differential equation of pollutant transport. It is the finite volume method, which is the object of advanced research, in view of the improvements that are ...
Marcello Benedini, George Tsakiris
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Beside the finite difference and finite element methods, a new numerical method has been recently proposed, which looks to be very promising for stable and reliable solutions of the fundamental differential equation of pollutant transport. It is the finite volume method, which is the object of advanced research, in view of the improvements that are ...
Marcello Benedini, George Tsakiris
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2016
The finite volume method is a more recent method than both finite difference and finite element methods. It is widely used in practice for example in fluid dynamics computations. We present the method in the simplest possible settings, first for one-dimensional elliptic problems, then for the transport equation in one and two dimensions. For the latter,
Hervé Le Dret, Brigitte Lucquin
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The finite volume method is a more recent method than both finite difference and finite element methods. It is widely used in practice for example in fluid dynamics computations. We present the method in the simplest possible settings, first for one-dimensional elliptic problems, then for the transport equation in one and two dimensions. For the latter,
Hervé Le Dret, Brigitte Lucquin
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Finite Element and Finite Volume Methods
2009In this chapter we consider finite element and finite volume discretisations of $$Lu\,: = - \varepsilon u'' - bu' + cu = f\,\,{\rm in}\,(0,1), \,\,\ u(0) = u (1) = 0,$$ with b ≥ β > 0. Its associated variational formulation is: Find \(u \in H_0^1 (0,1)\) such that $$a(u, v) = f(v)\,\,\, {\rm for\, all}\,\, v \in H_0^1 (0,1),$$ (5.2 ...
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2014
The finite volume method is a very popular method for the space discretization of partial differential problems in conservation form. For an in-depth presentation of the method, we suggest the monographs [LeV02a], [Wes01] and [Tor09].
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The finite volume method is a very popular method for the space discretization of partial differential problems in conservation form. For an in-depth presentation of the method, we suggest the monographs [LeV02a], [Wes01] and [Tor09].
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