Application of factor difference scheme to solving discrete flow equations based on unstructured grid

2009 ◽  
Vol 15 (5) ◽  
pp. 324-329
Author(s):  
Zhengxian Liu ◽  
Xuejun Wang ◽  
Jishuang Dai ◽  
Chuhua Zhang
Keyword(s):  
Difference Scheme ◽  
Unstructured Grid ◽  
Flow Equations ◽  
Discrete Flow ◽  
Factor Difference

scholarly journals Discrete flow mapping: transport of phase space densities on triangulated surfaces

2013 ◽  
Vol 469 (2155) ◽  
pp. 20130153 ◽  
Author(s):  
David J. Chappell ◽  
Gregor Tanner ◽  
Dominik Löchel ◽  
Niels Søndergaard
Keyword(s):  
Phase Space ◽  
Large Scale ◽  
Weather Forecasting ◽  
Linear Wave ◽  
Hamiltonian Vector Field ◽  
Flow Mapping ◽  
Space Applications ◽  
Flow Equations ◽  
Triangulated Surfaces ◽  
Discrete Flow

Energy distributions of high-frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics, vibroacoustics, seismology, electromagnetics and quantum mechanics. Related flow problems based on general conservation laws are used, for example, in weather forecasting or in molecular dynamics simulations. Solutions to these flow equations are often large-scale, complex and high-dimensional, leading to formidable challenges for numerical approximation methods. This paper presents an efficient and widely applicable method, called discrete flow mapping , for solving such problems on triangulated surfaces. An application in structural dynamics, determining the vibroacoustic response of a cast aluminium car body component, is presented.

scholarly journals Transonic Turbomachinery Calculations Using a Hybrid Structured-Unstructured Grid Method

1994 ◽  
Author(s):  
Scott M. Richardson
Keyword(s):  
Unstructured Grid ◽  
Unstructured Mesh ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Grid Method ◽  
Navier Stokes ◽  
Flow Equations ◽  
Transonic Compressor ◽  
Flow Features ◽  
Grid Points

A method is presented for solving the two-dimensional Navier-Stokes equations on a solution-adaptive grid of both structured and unstructured meshes. Flow near airfoil surfaces is modeled using an implicit finite difference algorithm on a structured O-type mesh. The flow equations in the blade passages are written in a cell-vertex finite volume formulation and are solved on an unstructured mesh using a Runge-Kutta explicit algorithm. Both the structured and unstructured grid also include solution dependent adaptation to allow resolution of flow features with a minimum of grid points. The structured mesh divides to locally add grid lines, while the unstructured mesh allows the addition or removal of individual cells. An overlapping interface region is used to conservatively communicate flow variable information between the two grids. The quasi-three-dimensional effects of streamtube contraction and radius change are included to allow calculation of modern turbomachine designs. A study is included to determine the effect on cacade parameters of inclusion of viscous terms in the solution of the flow equations in the unstructured domain. Quasi-three-dimensional computations of flow through a transonic compressor and turbine cascade are compared with experimental data.

Symmetrizable Difference Dchemes

2005 ◽  
Vol 5 (1) ◽  
pp. 3-50 ◽  
Author(s):  
Alexei A. Gulin
Keyword(s):  
Initial Data ◽  
Difference Scheme ◽  
Difference Schemes ◽  
Time Dependent ◽  
Stability Boundaries ◽  
Typical Representative ◽  
Variable Weight ◽  
The Stability ◽  
Conditions Of Stability ◽  
The Right

AbstractA review of the stability theory of symmetrizable time-dependent difference schemes is represented. The notion of the operator-difference scheme is introduced and general ideas about stability in the sense of the initial data and in the sense of the right hand side are formulated. Further, the so-called symmetrizable difference schemes are considered in detail for which we manage to formulate the unimprovable necessary and su±cient conditions of stability in the sense of the initial data. The schemes with variable weight multipliers are a typical representative of symmetrizable difference schemes. For such schemes a numerical algorithm is proposed and realized for constructing stability boundaries.

Difference Schemes for Nonlinear BVPS on the Semiaxis

2007 ◽  
Vol 7 (1) ◽  
pp. 25-47 ◽  
Author(s):  
I.P. Gavrilyuk ◽  
M. Hermann ◽  
M.V. Kutniv ◽  
V.L. Makarov
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Boundary Value Problem ◽  
Difference Scheme ◽  
Adaptive Algorithm ◽  
Order Differential Equation ◽  
Constructive Method ◽  
Numerical Examples ◽  
Exact Difference ◽  
The Given

Abstract The scalar boundary value problem (BVP) for a nonlinear second order differential equation on the semiaxis is considered. Under some natural assumptions it is shown that on an arbitrary finite grid there exists a unique three-point exact difference scheme (EDS), i.e., a difference scheme whose solution coincides with the projection of the exact solution of the given differential equation onto the underlying grid. A constructive method is proposed to derive from the EDS a so-called truncated difference scheme (n-TDS) of rank n, where n is a freely selectable natural number. The n-TDS is the basis for a new adaptive algorithm which has all the advantages known from the modern IVP-solvers. Numerical examples are given which illustrate the theorems presented in the paper and demonstrate the reliability of the new algorithm.

Dilation-free solutions for the incompressible flow equations on nonstaggered grids

AIAA Journal ◽  
1997 ◽  
Vol 35 ◽  
pp. 585-586
Author(s):  
P. A. Russell ◽  
S. Abdallah
Keyword(s):  
Incompressible Flow ◽  
Flow Equations
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