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Showing 1 to 13 of 13 for “"Finite volume schemes"”.
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Finite volume schemes for hyperbolic-parabolic systems : error estimates
Finite-volume schemes on unstructured grids are the most frequently used <br>to approximate solutions of systems of hyperbolic balance laws in multi-space dimension. <br>The convergence analysis for the scalar case is well developed, even though <br>not complete up to now. In contrast, very few is …
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Efficient finite-volume schemes for magnetohydrodynamic simulations in solar physics
We present efficient finite-volume schemes for solving the equations of (compressible) magnetohydrodynamics (MHD) in one, two, and three spatial dimensions. We introduce a new approximate Riemann solver for the ideal gas MHD equations (MHD-HLLEM) that outperforms all other solvers considered. We …
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Unstructured h-adaptive finite volume schemes for compressible viscous fluid flow
… The spatial discretization is based on a finite volume scheme for two- and three-dimensional flow problems. Thereby, the grid is considered as a fully unstructured mesh, composed of simply connected elements with otherwise arbitrary topology. The method is of second order accuracy in space …
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High-order well-balanced finite volume schemes for geophysical flows : development and numerical comparisons
… first part of this thesis we present a class of schemes of any desired order of accuracy which preserve the lake at rest perfectly. These schemes should have an impact for studying important classes of lake and ocean flows. In the Introduction we present some of the key ideas and ingredients of …
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Well balanced Arbitrary-Lagrangian-Eulerian Finite Volume schemes on moving nonconforming meshes for non-conservative Hyperbolic systems
… direct Arbitrary-Lagrangian-Eulerian (ALE) Finite Volume scheme for nonlinear hyperbolic systems, written both in conservative and non-conservative form, whose peculiarity is the nonconforming motion of interfaces. Moreover it has been coupled together with specifically designed …
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Error estimates for numerical approximations to scalar conservation laws
… and a-posteriori error estimates <br>for certain finite volume approximations of scalar hyperbolic conservation laws. <br>We introduce a new technique to prove a-priori error estimates which is based <br>on a duality argument and involves a consistency error of cell averages. <br>Next, we …
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Particles methods for kinetic equations in plasma physics, collective behaviors and optimization.
… deterministic methods, such as Lagrangian schemes, Galerkin schemes and finite volume schemes, an important attention is given to particles schemes. These methods are able to produce a good approximation of the density function, and, by introducing stochasticity, they are able to capture …
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Die Runge-Kutta-Discontinuous-Galerkin-Methode zur Lösung konvektionsdominierter tiefengemittelter Flachwasserprobleme
… with a Runge-Kutta-Discontinuous-Galerkin finite-element method. As a background, a detailed discussion of the mathematical and physical properties of the governing equations is given with particular attention to discontinuous solutions. Existing numerical schemes are reviewed and …
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The development of dedicated CFD solver for aerodynamic analysis on internal and external flow
… present work focuses on the use of two types of Finite Volume methods. The first Finite volume method is a Cell-Centered Finite volume Scheme, while the second one is the Roe’s Finite Volume Scheme. In parallel to the development of computer code based on finite volume schemes, the present works …
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Numerical Methods for Compressible Multi-phase flows with Surface Tension
… capturing Total Variation Diminishing (TVD) finite volume scheme is used on both Cartesian and unstructured triangular grids. Regarding the TVD finite volume scheme on the unstructured grid, time-accurate local time stepping (LTS) is applied to compute the solutions of the governing PDE …
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Semi-implicit schemes for compressible fluids in elastic pipes and a-posteriori sub-cell finite volume limiting techniques for semi-implicit Discontinuous Galerkin schemes for hyperbolic conservation laws on staggered meshes
… on staggered meshes applied both to the class of finite volume (FV) and both to the family of high order Discontinuous Galerkin (DG) finite elements schemes. In particular, we want to show that these new semi-implicit schemes can be applied in several fields of applied sciences, such as in …
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Parallel dynamic load-balancing for adaptive distributive memory PDE solvers
… in parallel solutions based upon either finite element or finite volume schemes on unstructured grids and we assume that geometric parallelism is used, whereby the finite element or finite volume grids are partitioned across the available parallel processors. For parallel efficiency it is …
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Two-phase two-fluid model solver based on a high-resolution total variation diminishing scheme
… scheme is unconditionally stable (1/2≤theta≤1). Finite volume techniques with staggered mesh are then used to develop a solver for the one-dimensional two-phase two-fluid model based on different numerical schemes including the new scheme developed here. Linearized equations of state are used as …