The Cauchy-Lagrangian method for numerical analysis of Euler flow

JOURNAL OF COMPUTATIONAL PHYSICS

卷:306

Article

Podvigina, O.¹  Zheligovsky, V.¹  Frisch, U.² 

[1] Russian Acad Sci, Inst Earthquake Predict Theory & Math Geophys, Moscow 117997, Russia

[2] CNRS, Lab Lagrange, UCA, OCA,CS 34229, F-06304 Nice 4, France

关键词: Euler equation;    Lagrangian coordinates;    Cauchy invariants;    Semi-Lagrangian methods;    High-order temporal schemes;    High-precision schemes;   

DOI  :  10.1016/j.jcp.2015.11.045

来源: Elsevier

【 摘 要 】

A novel semi-Lagrangian method is introduced to solve numerically the Euler equation for ideal incompressible flow in arbitrary space dimension. It exploits the time-analyticity of fluid particle trajectories and requires, in principle, only limited spatial smoothness of the initial data. Efficient generation of high-order time-Taylor coefficients is made possible by a recurrence relation that follows from the Cauchy invariants formulation of the Euler equation (Zheligovsky and Frisch, 2014 [44]). Truncated time-Taylor series of very high order allow the use of time steps vastly exceeding the Courant-Friedrichs-Lewy limit, without compromising the accuracy of the solution. Tests performed on the two-dimensional Euler equation indicate that the Cauchy-Lagrangian method is more - and occasionally much more - efficient and less prone to instability than Eulerian Runge-Kutta methods, and less prone to rapid growth of rounding errors than the high-order Eulerian time-Taylor algorithm. We also develop tools of analysis adapted to the Cauchy-Lagrangian method, such as the monitoring of the radius of convergence of the time-Taylor series. Certain other fluid equations can be handled similarly. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free