High-Order WENO Finite Volume Methods on Cartesian Grids with Adaptive Mesh Refinement PDF Download
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Author: Pawel Buchmüller
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Author: Pawel Buchmüller
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 12
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Book Description
A fourth-order accurate finite-volume method is presented for solving time-dependent hyperbolic systems of conservation laws on mapped grids that are adaptively refined in space and time. Novel considerations for formulating the semi-discrete system of equations in computational space combined with detailed mechanisms for accommodating the adapting grids ensure that conservation is maintained and that the divergence of a constant vector field is always zero (freestream-preservation property). Advancement in time is achieved with a fourth-order Runge-Kutta method.
Author: Luigi Brugnano
Publisher: MDPI
ISBN: 3038976660
Category : Juvenile Nonfiction
Languages : en
Pages : 306
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Book Description
The use of scientific computing tools is currently customary for solving problems at several complexity levels in Applied Sciences. The great need for reliable software in the scientific community conveys a continuous stimulus to develop new and better performing numerical methods that are able to grasp the particular features of the problem at hand. This has been the case for many different settings of numerical analysis, and this Special Issue aims at covering some important developments in various areas of application.
Author: Yong-Tao Zhang
Publisher:
ISBN:
Category : Computational grids (Computer systems)
Languages : en
Pages : 38
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Book Description
In this paper we construct high order weighted essentially non-oscillatory (WENO) schems for solving the nonlinear Hamilton-Jacobi equations on two-dimensional unstructured meshes. The main ideas are nodal based approximations, the usage of monotone Hamiltonians as building blocks on unstructured meshes, nonlinear weights using smooth indicators of second and higher derivatives, and a strategy to choose diversified smaller stencils to make up the bigger stencil in the WENO procedure. Both third-order and fourth-order WENO schemes using combinations of second-order approximations with nonlinear weights are constructed. Extensive numerical experiments are performed to demonstrate the stability and accuracy of the methods. High-order accuracy in smooth regions, good resolution of derivative singularities, and convergence to viscosity solutions are observed.
Author: Christian Klingenberg
Publisher: Springer
ISBN: 3319915452
Category : Mathematics
Languages : en
Pages : 685
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Book Description
The first of two volumes, this edited proceedings book features research presented at the XVI International Conference on Hyperbolic Problems held in Aachen, Germany in summer 2016. It focuses on the theoretical, applied, and computational aspects of hyperbolic partial differential equations (systems of hyperbolic conservation laws, wave equations, etc.) and of related mathematical models (PDEs of mixed type, kinetic equations, nonlocal or/and discrete models) found in the field of applied sciences.
Author: Lucian Ivan
Publisher:
ISBN: 9780494778326
Category :
Languages : en
Pages :
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Author: Hans Svend Johansen
Publisher:
ISBN:
Category :
Languages : en
Pages : 408
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Author: Chi-Wang Shu
Publisher:
ISBN:
Category : Finite differences
Languages : en
Pages : 24
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Book Description
In recent years high order numerical methods have been widely used in computational fluid dynamics (CFD), to effectively resolve complex flow features using meshes which are reasonable for today's computers. In this paper we review and compare three types of high order methods being used in CFD, namely the weighted essentially non-oscillatory (WENO) finite difference methods, the WENO finite volume methods, and the discontinuous Galerkin (DG) finite element methods. We summarize the main features of these methods, from a practical user's point of view, indicate their applicability and relative strength, and show a few selected numerical examples to demonstrate their performance on illustrative model CFD problems.
Author: John E. Melton
Publisher:
ISBN:
Category :
Languages : en
Pages : 392
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Author: Jenmy Zimi Zhang
Publisher:
ISBN: 9780494766118
Category :
Languages : en
Pages : 224
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Book Description
A novel anisotropic adaptive mesh refinement (AMR) technique is proposed and de- scribed. A block-based AMR approach is used which permits highly efficient and scalable implementations on parallel computer architectures and the use of multi-block, body-fitted computational grids for the treatment of complex geometries. However, rather than adopting the more usual isotropic approach to the refinement of the grid blocks, the proposed approach uses a binary hierarchical tree data structure that allows for anisotropic refinement of the grid blocks in each of the coordinate directions in an inde- pendent fashion. This allows for more efficient and accurate treatment of narrow layers, discontinuities, and/or shocks in the solutions which occur, for example, in the thin boundary and mixing layers of high-Reynolds-number viscous flows and in the regions of strong non-linear wave interactions of high-speed compressible flows with shocks. The anisotropic AMR technique is implemented within an existing finite-volume framework, which encompasses both explicit and implicit solution methods, and is capable of per- forming calculations with both second- and higher-order spatial accuracy. To clearly demonstrate the potential and feasibility of the proposed AMR technique, it is applied to the unsteady and steady-state solutions of both a model system, the advection diffusion equation, as well as the Euler equations governing compressible, inviscid, gaseous flows, both in two space dimensions.
