Boundary Closures for Sixth-Order Energy-Stable Weighted Essentially Non-Oscillatory Finite-Difference Schemes

2013 ◽  
pp. 117-160 ◽  
Author(s):  
Mark H. Carpenter ◽  
Travis C. Fisher ◽  
Nail K. Yamaleev
Keyword(s):  
Finite Difference ◽  
Difference Schemes ◽  
Sixth Order ◽  
Finite Difference Schemes ◽  
Order Energy ◽  
Energy Stable

scholarly journals Boundary closures for fourth-order energy stable weighted essentially non-oscillatory finite-difference schemes

2011 ◽  
Vol 230 (10) ◽  
pp. 3727-3752 ◽  
Author(s):  
Travis C. Fisher ◽  
Mark H. Carpenter ◽  
Nail K. Yamaleev ◽  
Steven H. Frankel
Keyword(s):  
Finite Difference ◽  
Fourth Order ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Order Energy ◽  
Energy Stable

scholarly journals A Family of Sixth-Order Compact Finite-Difference Schemes for the Three-Dimensional Poisson Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Yaw Kyei ◽  
John Paul Roop ◽  
Guoqing Tang
Keyword(s):  
Finite Difference ◽  
High Performance ◽  
Three Dimensional ◽  
Difference Schemes ◽  
Poisson’S Equation ◽  
Sixth Order ◽  
Finite Difference Schemes ◽  
Poisson's Equation ◽  
Compact Finite Difference ◽  
Compact Finite Difference Schemes

We derive a family of sixth-order compact finite-difference schemes for the three-dimensional Poisson's equation. As opposed to other research regarding higher-order compact difference schemes, our approach includes consideration of the discretization of the source function on a compact finite-difference stencil. The schemes derived approximate the solution to Poisson's equation on a compact stencil, and thus the schemes can be easily implemented and resulting linear systems are solved in a high-performance computing environment. The resulting discretization is a one-parameter family of finite-difference schemes which may be further optimized for accuracy and stability. Computational experiments are implemented which illustrate the theoretically demonstrated truncation errors.

scholarly journals SIXTH-ORDER ACCURATE FINITE DIFFERENCE SCHEMES FOR THE HELMHOLTZ EQUATION

2006 ◽  
Vol 14 (03) ◽  
pp. 339-351 ◽  
Author(s):  
I. SINGER ◽  
E. TURKEL
Keyword(s):  
Finite Difference ◽  
Helmholtz Equation ◽  
Truncation Error ◽  
Model Problem ◽  
Difference Schemes ◽  
Sixth Order ◽  
Finite Difference Schemes ◽  
Local Truncation Error ◽  
Two Dimensional ◽  
Truncation Order

We develop and analyze finite difference schemes for the two-dimensional Helmholtz equation. The schemes which are based on nine-point approximation have a sixth-order accurate local truncation order. The schemes are compared with the standard five-point pointwise representation, which has second-order accurate local truncation error and a nine-point fourth-order local truncation error scheme based on a Padé approximation. Numerical results are presented for a model problem.

scholarly journals Accurate Simulation of Contaminant Transport Using High-Order Compact Finite Difference Schemes

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Gurhan Gurarslan
Keyword(s):  
Finite Difference ◽  
Exact Solutions ◽  
Contaminant Transport ◽  
High Order ◽  
Difference Schemes ◽  
Sixth Order ◽  
High Order Accuracy ◽  
Finite Difference Schemes ◽  
Compact Finite Difference ◽  
Compact Finite Difference Schemes

Numerical simulation of advective-dispersive contaminant transport is carried out by using high-order compact finite difference schemes combined with second-order MacCormack and fourth-order Runge-Kutta schemes. Both of the two schemes have accuracy of sixth-order in space. A sixth-order MacCormack scheme is proposed for the first time within this study. For the aim of demonstrating efficiency and high-order accuracy of the current methods, some numerical experiments have been done. The schemes are implemented to solve two test problems with known exact solutions. It has been exhibited that the methods are capable of succeeding high accuracy and efficiency with minimal computational effort, by comparisons of the computed results with exact solutions.

Comparison of Two Sixth-Order Compact Finite Difference Schemes for Burgers' Equation

2013 ◽  
Vol 444-445 ◽  
pp. 681-686
Author(s):  
Xiao Gang He ◽  
Ying Yang ◽  
Ping Zhang ◽  
Xiao Hua Zhang
Keyword(s):  
Finite Difference ◽  
Burgers Equation ◽  
Difference Schemes ◽  
Sixth Order ◽  
Finite Difference Schemes ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Compact Finite Difference ◽  
Small Viscosity ◽  
Compact Finite Difference Schemes

In this study, two sixth-order compact finite difference schemes have been considered for solving the Burgers equation. The main difference of these schemes lies in the calculation of second-order derivative terms, which is obtained by applying the first-order operator twice and the method of undetermined coefficients. The aim is to comparison these schemes in terms of computational accuracy for solving the Burgers equation with difference viscosity values, especially for very small viscosity values. The results show that both schemes achieve almost the same accuracy for large viscosity values and second method is more accurate for moderate viscosity values, but both schemes are failed for very small viscosity values. However, when both schemes coupled low-pass filter for very small viscosity values, both schemes can well inhibit the problem.

Sign in / Sign up

Export Citation Format

Share Document