A numerical third-order method for solving the Navier–Stokes equations with respect to time

V. G. Krupa

Baranov Central Institute of Aviation Motor Development, Moscow, 111116 Russia

Abstract: A linearly implicit (Rosenbrock-type) numerical method for the integration of three-dimensional Navier–Stokes equations for compressible fluid with respect to time is proposed. The method has four stages and third order of accuracy with respect to time. As the benchmark, the Cauchy problem on a 3D torus is solved. The computed distributions are compared with the solution specified by the ABC flow.

Key words: linearly implicit Runge–Kutta method, Rosenbrock method, W-method, Navier–Stokes equations, ABC flowю.

UDC: 519.635

Received: 01.04.2019
Revised: 01.07.2019
Accepted: 08.07.2019

DOI: 10.1134/S0044466919110085

 English version: Computational Mathematics and Mathematical Physics, 2019, 59:11, 1881–1892

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