A New High-Order Compact Scheme of Unstructured Finite Volume Method

2016 ◽  
Vol 13 (05) ◽  
pp. 1650022
Author(s):  
Lei Fu ◽  
Shuai Zhang ◽  
Yao Zheng
Keyword(s):  
High Order ◽  
Compact Scheme ◽  
Benchmark Problems ◽  
High Order Scheme ◽  
Gradient Reconstruction ◽  
Order Scheme ◽  
Volume Method ◽  
Unstructured Finite Volume Method ◽  
High Order Compact Scheme ◽  
Good Agreement

A compact high-order scheme has been successfully proposed and verified in this paper. In this scheme, the traditional gradient reconstruction was replaced with a compact scheme. There were no needs to modify the process and algorithms of unstructured FVM including boundary conditions, flux technique, limiter functions and so on. Both memory and computation loads with the new scheme were not increased than the traditional one. Additionally, we modified Venkatakrishnan limiter to suppress numerical oscillation. The proposed compact scheme and modified Venkatakrishnan limiter have been verified with numerical experiments on benchmark problems. Numerical results showed good agreement with those obtained by other methods.

scholarly journals Grid Average and Nodal Value in High Order Scheme

2018 ◽  
Vol 35 (3) ◽  
pp. 335-342
Author(s):  
Z. Liu ◽  
Q. Cai
Keyword(s):  
Truncation Error ◽  
Absolute Error ◽  
High Order ◽  
Fine Grid ◽  
Order Of Accuracy ◽  
High Order Scheme ◽  
High Order Schemes ◽  
Order Scheme ◽  
The Absolute ◽  
Volume Method

ABSTRACTThe concepts of nodal value and grid average in cell centered finite volume method (FVM) are clarified in this work, strict distinction between the two concepts in constructing numerical schemes is made, and common fault in misidentifying the two concepts is pointed out. The expansion based on grid average, similar to Taylor’s expansion, is deduced to construct correct scheme in terms of grid average and to obtain modified partial differential equation (MPDE) which determines the order of accuracy of numerical scheme theoretically. Correct high order scheme, taking QUICK (Quadratic Upstream Interpolation for Convective Kinematics) scheme as an example, is constructed in different approaches. Furthermore, the property of interpolation coefficients is analyzed. We also pointed out that for high order schemes, round-off error dominates the absolute error in fine grid and truncation error dominates the absolute error in coarse grid.

HIGH-ORDER SCHEME IMPLEMENTATION USING NEWTON-KRYLOV SOLUTION METHODS

1997 ◽  
Vol 31 (3) ◽  
pp. 295-312 ◽  
Author(s):  
Richard W. Johnson ◽  
Paul R. McHugh ◽  
Dana A. Knoll
Keyword(s):  
High Order ◽  
High Order Scheme ◽  
Solution Methods ◽  
Order Scheme

scholarly journals 3D Finite Volume Modeling of ENDE Using ElectromagneticT-Formulation

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Yue Li ◽  
Gérard Berthiau ◽  
Mouloud Feliachi ◽  
Ahmed Cheriet
Keyword(s):  
Finite Volume ◽  
Maxwell Equations ◽  
Benchmark Problems ◽  
Work Piece ◽  
Impedance Change ◽  
Improved Method ◽  
Inconel 600 ◽  
Volume Modeling ◽  
Volume Method ◽  
Good Agreement

An improved method which can analyze the eddy current density in conductor materials using finite volume method is proposed on the basis of Maxwell equations andT-formulation. The algorithm is applied to solve 3D electromagnetic nondestructive evaluation (E’NDE) benchmark problems. The computing code is applied to study an Inconel 600 work piece with holes or cracks. The impedance change due to the presence of the crack is evaluated and compared with the experimental data of benchmark problems No. 1 and No. 2. The results show a good agreement between both calculated and measured data.

S1910103 Computation of Forced Turbulent Flow over Reentry Capsule Afterbody with High Order Scheme

2014 ◽  
Vol 2014 (0) ◽  
pp. _S1910103--_S1910103-
Author(s):  
Tomoaki Ishihara ◽  
Yousuke Ogino ◽  
Naofumi Ohnishi ◽  
Keisuke Sawada ◽  
Hideyuki Tanno
Keyword(s):  
Turbulent Flow ◽  
High Order ◽  
High Order Scheme ◽  
Order Scheme

scholarly journals On the Integration Schemes of Retrieving Impulse Response Functions from Transfer Functions

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Kui Fu Chen ◽  
Yan Feng Li
Keyword(s):  
Numerical Integration ◽  
Transfer Functions ◽  
Sampling Interval ◽  
High Order ◽  
Impulse Response Functions ◽  
Inverse Laplace Transformation ◽  
High Order Scheme ◽  
Integration Schemes ◽  
Order Scheme ◽  
Better Than

The numerical inverse Laplace transformation (NILM) makes use of numerical integration. Generally, a high-order scheme of numerical integration renders high accuracy. However, surprisingly, this is not true for the NILM to the transfer function. Numerical examples show that the performance of higher-order schemes is no better than that of the trapezoidal scheme. In particular, the solutions from high-order scheme deviate from the exact one markedly over the rear portion of the period of interest. The underlying essence is examined. The deviation can be reduced by decreasing the frequency-sampling interval.

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