Energy conservation uncertainly due to the use of an implicit time integration method clarified by a multiplexed TGV inviscid flow

• Published in: Journal of physics. Conference series Vol. 2701; no. 1; pp. 12059 - 12064
• Main Authors: Chitose, Makoto, Suzuki, Hiroki, Kouchi, Toshinori
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.02.2024
• Subjects: Boundary conditions; Conservation; Errors; Exact solutions; Inviscid flow; Kinetic energy; Multiplexing; Runge-Kutta method; Time integration; Two dimensional flow; Wavelengths
• ISSN: 1742-6588; 1742-6596; 1742-6596
• DOI: 10.1088/1742-6596/2701/1/012059

This study attempts to elucidate the conservation errors induced by the implicit time integration method within a multiscale flow. Using the multiplexed Taylor analytical solution as the initial field, three distinct multiscale turbulence fields were formulated, each characterised by different wavenumber attributes. A two-dimensional inviscid flow field, replicated in a computational domain with a side of 2π and subject to periodic boundary conditions, was used to illuminate kinetic energy conservation errors. The implicit time integration method - specifically the second-order accurate Crank-Nicolson method - was compared with explicit methods, such as the second-order accurate Adams-Bashforth and third-order accurate Runge-Kutta methods. The study also examines the differences between the analytical Taylor solution and a random flow field, particularly in their satisfaction of the Navier-Stokes equations and wavenumber composition, while highlighting the need for preliminary analysis for random flow fields prior to validation calculations.