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Analytical linear numerical stability conditions for an anisotropic three-dimensional advection-diffusion equation
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TLDR
In this paper, a one-timestep scheme for advective-diffusive problems in three dimensions is analyzed from a numerical stability point of view, and the amplification factor of the von Neumann method is calculated, and necessary and sufficient conditions for the general one-dimensional problem are retrieved.Abstract:
A one-timestep scheme for advective-diffusive problems in three dimensions is analysed from a numerical stability point of view. Choosing a realizable general seven-point centred discretization scheme, the amplification factor of the von Neumann method is calculated, and necessary and sufficient stability conditions for the general one-dimensional problem are retrieved. A similar analysis then leads to necessary conditions for the three-dimensional case. It is proved that the conditions obtained are also sufficient for an explicit N-dimensional case. Generalization is made to uncentered schemes and some classical results are recovered or corrected. For practical use, some miminum implicit factors necessary for stability are calculated and it is shown that the inspection of one-dimensional problems to get stability conditions can be tricky.read more
Citations
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Several new numerical methods for compressible shear-layer simulations
TL;DR: Results indicate that the Runge–Kutta integrators did not possess sufficient dissipation to be useful candidates for the computation of variable-density compressible shear layers at the levels of resolution used in the current work.
Comparison of Several Numerical Methods for Simulation of Compressible Shear Layers
TL;DR: In this article, several numerical integration schemes with various temporal accuracies and arbitrary spatial accuracies for both inviscid and viscous terms are presented and analyzed using explicit or compact finite-difference derivative operators.
Journal ArticleDOI
A conservative orbital advection scheme for simulations of magnetized shear flows with the PLUTO code
TL;DR: In this paper, a robust numerical scheme was proposed to overcome the Courant condition by improving and extending the FARGO (fast advection in rotating gaseous objects) to the equations of magnetohydrodynamics (MHD) using a more general formalism.
Journal ArticleDOI
Graphical notation reveals topological stability criteria for collective dynamics in complex networks.
TL;DR: A graphical notation by which certain spectral properties of complex systems can be rewritten concisely and interpreted topologically is proposed and it is shown that in systems such as the Kuramoto model the Coates graph of the Jacobian matrix must contain a spanning tree of positive elements to be locally stable.
Journal ArticleDOI
Forces and torques on a prolate spheroid: low-Reynolds-number and attack angle effects
TL;DR: The 3D flow field around a prolate spheroid has been obtained by integration of the full Navier-Stokes equations at Reynolds numbers 0.1, 1.0, and 10.
References
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Journal ArticleDOI
Systems of conservation laws
Peter D. Lax,Burton Wendroff +1 more
TL;DR: In this article, a wide class of difference equations is described for approximating discontinuous time dependent solutions, with prescribed initial data, of hyperbolic systems of nonlinear conservation laws, and the best ones are determined, i.e., those which have the smallest truncation error and in which the discontinuities are confined to a narrow band of 2-3 meshpoints.
Book
Methods of Numerical Mathematics
TL;DR: In this paper, the authors present a general approach to the construction of subspaces of piecewise-polynomial functions, based on the Galerkin (Finite Elements) method.
Journal ArticleDOI
The modified equation approach to the stability and accuracy analysis of finite-difference methods
R. F. Warming,B.J Hyett +1 more
TL;DR: In this paper, the stability and accuracy of finite-difference approximations to simple linear PDEs are analyzed by studying the modified partial differential equation, which is derived by first expanding each term of a difference scheme in a Taylor series and then eliminating time derivatives higher than first order by certain algebraic manipulations.