Journal ArticleDOI
Summation by parts operators for finite difference approximations of second derivatives
Ken Mattsson,Jan Nordström +1 more
TLDR
In this article, a finite difference operator approximating second derivatives and satisfying a summation by parts rule was derived for the fourth, sixth and eighth order case by using the symbolic mathematics software Maple.About:
This article is published in Journal of Computational Physics.The article was published on 2004-09-20. It has received 394 citations till now. The article focuses on the topics: Summation by parts & Second derivative.read more
Citations
More filters
Journal ArticleDOI
Review of summation-by-parts schemes for initial–boundary-value problems
Magnus Svärd,Jan Nordström +1 more
TL;DR: This paper will review the development of high order accurate multi-block finite difference schemes, point out the main contributions and speculate about the next lines of research in this area.
Journal ArticleDOI
Mimetic finite difference method
TL;DR: Flexibility and extensibility of the mimetic methodology are shown by deriving higher-order approximations, enforcing discrete maximum principles for diffusion problems, and ensuring the numerical stability for saddle-point systems.
Journal ArticleDOI
Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations
TL;DR: A brief history of SBP-SAT methods can be found in this paper, where a methodology for deriving SBP operators for first derivatives and second derivatives with variable coefficients is also provided.
Journal ArticleDOI
High-order entropy stable finite difference schemes for nonlinear conservation laws
TL;DR: A comparison technique is used to derive a new Entropy Stable Weighted Essentially Non-Oscillatory (SSWENO) finite difference method, appropriate for simulations of problems with shocks.
Journal ArticleDOI
A stable high-order finite difference scheme for the compressible Navier-Stokes equations, far-field boundary conditions
TL;DR: This work constructs a stable high-order finite difference scheme for the compressible Navier-Stokes equations, that satisfy an energy estimate, and shows the theoretical third-, fourth-, and fifth-order convergence rate, for a viscous shock, where the analytic solution is known.
References
More filters
BookDOI
Time Dependent Problems and Difference Methods
TL;DR: Time-Dependent Problems and Difference Methods, Second Edition as discussed by the authors provides guidance for the analysis of difference methods for computing approximate solutions to partial differential equations for time-dependent problems, and provides a more useful analysis of numerical methods.
Journal ArticleDOI
Summation by parts for finite difference approximations for d/dx
TL;DR: In this article, the authors presented a multi-parameter family of difference operators when τ⩾3, where τ is the dimension of the difference operator and λ is the number of points in the difference matrix.
Journal ArticleDOI
Low-Dissipative High-Order Shock-Capturing Methods Using Characteristic-Based Filters
TL;DR: In this paper, an approach which closely maintains the non-dissipative nature of classical fourth or higher-order spatial differencing away from shock waves and steep gradient regions while being capable of accurately capturing discontinuities, steep gradient, and fine scale turbulent structures in a stable and efficient manner is described.
Journal ArticleDOI
A Stable and Conservative Interface Treatment of Arbitrary Spatial Accuracy
TL;DR: In this paper, the authors derived stable and accurate interface conditions based on the SAT penalty method for the linear advection?diffusion equation, which are functionally independent of the spatial order of accuracy and rely only on the form of the discrete operator.