scholarly journals High-order compact LOD methods for solving high-dimensional advection equations

2021 ◽  
Vol 40 (3) ◽  
Author(s):  
Bo Hou ◽  
Yongbin Ge
Keyword(s):  
Truncation Error ◽  
Three Dimensional ◽  
Taylor Series Expansion ◽  
High Order ◽  
High Dimensional ◽  
Analysis Method ◽  
Order Accuracy ◽  
Von Neumann ◽  
One Dimensional ◽  
Von Neumann Analysis

AbstractIn this paper, by using the local one-dimensional (LOD) method, Taylor series expansion and correction for the third derivatives in the truncation error remainder, two high-order compact LOD schemes are established for solving the two- and three- dimensional advection equations, respectively. They have the fourth-order accuracy in both time and space. By the von Neumann analysis method, it shows that the two schemes are unconditionally stable. Besides, the consistency and convergence of them are also proved. Finally, numerical experiments are given to confirm the accuracy and efficiency of the present schemes.

TRUNCATION ERROR REDUCTION METHOD FOR POISSON EQUATION

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1555-1558
Author(s):  
JIAN XIA ◽  
CHAOQUN LIU
Keyword(s):  
Poisson Equation ◽  
Iterative Process ◽  
Truncation Error ◽  
Reduction Method ◽  
Error Reduction ◽  
Coarse Grid ◽  
High Order ◽  
High Order Accuracy ◽  
Order Accuracy ◽  
Original Grid

A new so-called truncation error reduction method (TERM) is developed in this work. This is an iterative process which initially uses a coarse grid (2h) to estimate the truncation error and then reduces the error on the original grid (h). The purpose of this method is to use multigrid technique to achieve high-order accuracy on simple stencils.

Insights from von Neumann analysis of high-order flux reconstruction schemes

2011 ◽  
Vol 230 (22) ◽  
pp. 8134-8154 ◽  
Author(s):  
P.E. Vincent ◽  
P. Castonguay ◽  
A. Jameson
Keyword(s):  
High Order ◽  
Flux Reconstruction ◽  
Von Neumann ◽  
Von Neumann Analysis

HEGDE'S INTERFACE NUMERICAL TECHNIQUE FOR RESOLVING QUASI-ONE-DIMENSIONAL NOZZLE FLOWS

2009 ◽  
Vol 06 (01) ◽  
pp. 75-91
Author(s):  
GANESH S. HEGDE ◽  
G. M. MADHU
Keyword(s):  
Truncation Error ◽  
Numerical Solutions ◽  
Numerical Technique ◽  
Computational Cost ◽  
Optimal Solution ◽  
Taylor Series Expansion ◽  
Computational Effort ◽  
Navier Stokes Equation ◽  
One Dimensional ◽  
Interface Theory

Faster convergence, better accuracy and improved stability of the solutions to fluid flow and heat transfer problems in CFD reduce the computational cost and time. The numerical solutions to partial differential equations governing the physical flow and heat phenomena, using computer software and hardware, have been obtained by various techniques which have been refined over the years. The numerical techniques have obtained the base in finite difference method (FDM) approximations derived from Taylor series expansion. Because of linearization, FDM approximations have truncation error creeping into the values of the partial derivatives, which projects an unrealistic picture of the final outcome of results in terms of accuracy, convergence and stability. As the prime objective of this paper, the minimization of truncation error is attempted with the aid of the interface theory (briefly described in the appendix) used as a computational treatment tool. In simple terms, the interface theory provides an optimal solution to all variables in a linear indeterminate system with redundancy in unknowns. The effort has converged in the form of Hegde's interface numerical technique (HINT), which is demonstrated on a quasi-one-dimensional nozzle flow, the physical behavior of which is described by the Navier–Stokes equation considered specific to the said case. HINT could successfully match the results of MacCormack's predictor–corrector method as far as the accuracy is concerned, but with less computational effort and higher productivity. To the knowledge of the authors, HINT may be considered both original and different for its kind in the vast developments in CFD.

scholarly journals Development and Validation of a Three-Dimensional Diffusion Code Based on a High Order Nodal Expansion Method for Hexagonal-zGeometry

2016 ◽  
Vol 2016 ◽  
pp. 1-21 ◽  
Author(s):  
Daogang Lu ◽  
Chao Guo
Keyword(s):  
Order Approximation ◽  
Three Dimensional ◽  
Expansion Method ◽  
High Order ◽  
Quadratic Polynomial ◽  
Quadratic Approximation ◽  
Polynomial Expansion ◽  
Benchmark Problems ◽  
One Dimensional ◽  
Nodal Expansion Method

A three-dimensional, multigroup, diffusion code based on a high order nodal expansion method for hexagonal-zgeometry (HNHEX) was developed to perform the neutronic analysis of hexagonal-zgeometry. In this method, one-dimensional radial and axial spatially flux of each node and energy group are defined as quadratic polynomial expansion and four-order polynomial expansion, respectively. The approximations for one-dimensional radial and axial spatially flux both have second-order accuracy. Moment weighting is used to obtain high order expansion coefficients of the polynomials of one-dimensional radial and axial spatially flux. The partially integrated radial and axial leakages are both approximated by the quadratic polynomial. The coarse-mesh rebalance method with the asymptotic source extrapolation is applied to accelerate the calculation. This code is used for calculation of effective multiplication factor, neutron flux distribution, and power distribution. The numerical calculation in this paper for three-dimensional SNR and VVER 440 benchmark problems demonstrates the accuracy of the code. In addition, the results show that the accuracy of the code is improved by applying quadratic approximation for partially integrated axial leakage and four-order approximation for one-dimensional axial spatially flux in comparison to flat approximation for partially integrated axial leakage and quadratic approximation for one-dimensional axial spatially flux.

scholarly journals DECONFINEMENT AND COLD ATOMS IN OPTICAL LATTICES

2006 ◽  
Vol 20 (30n31) ◽  
pp. 5169-5178
Author(s):  
M. A CAZALILLA ◽  
A. F. HO ◽  
T. GIAMARCHI
Keyword(s):  
Optical Lattices ◽  
Cold Atoms ◽  
Three Dimensional ◽  
Optical Traps ◽  
High Dimensional ◽  
Interacting Particles ◽  
Controllable System ◽  
One Dimensional ◽  
Physical Systems ◽  
The One

Despite the fact that by now one dimensional and three dimensional systems of interacting particles are reasonably well understood, very little is known on how to go from the one dimensional physics to the three dimensional one. This is in particular true in a quasi-one dimensional geometry where the hopping of particles between one dimensional chains or tubes can lead to a dimensional crossover between a Luttinger liquid and more conventional high dimensional states. Such a situation is relevant to many physical systems. Recently cold atoms in optical traps have provided a unique and controllable system in which to investigate this physics. We thus analyze a system made of coupled one dimensional tubes of interacting fermions. We explore the observable consequences, such as the phase diagram for isolated tubes, and the possibility to realize unusual superfluid phases in coupled tubes systems.

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