Numerical investigation using an exact solution of the effects of non-solenoidality of the viscous terms on the incompressible flow

Self Cite

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.

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Chitose,

Suzuki,

Kouchi

2024

Self Cite

“…Previous studies that have validated OpenFOAM have used channel turbulence (e.g., [2]) and not Taylor-Green vortex (TGV) flows [10][11][12] for validation; TGV flows are unsteady turbulence unlike channel turbulence. Therefore, the use of TGV flows allows OpenFOAM to be validated in terms of unsteady fields.…”

Section: Introductionmentioning

confidence: 99%

Assessing OpenFOAM-based Large-eddy Simulation Using Decay Characteristics of An Isotropic Taylor-green Vortex

Ono,

Chitose,

Suzuki

et al. 2024

Self Cite

The aim of this study is to investigate OpenFOAM using isotropic TGV flows. The main focus is on the establishment of energy conservation laws, in particular using inviscid fields to assess energy constancy; Large-Eddy Simulation (LES) is applied and the results are compared with those obtained using spectral methods; unlike previous studies of OpenFOAM, this study uses an unsteady turbulent TGV flow. The computational methods used are a central difference method, a PISO algorithm and a Smagorinsky model. The study revealed errors in the conservation of kinetic energy in the OpenFOAM analysis. In particular, the energy decay was significant at high spatial resolution, confirming the different turbulence energy decay characteristics of DNS and OpenFOAM. However, when the model constant was 0.6, the decay characteristics were shown to be in good agreement with DNS.

“…The Taylor-Green vortex is often used as a benchmark for decaying turbulence [3]. Taylor's analytical solution is one of the analytical solutions for 2D flow fields and is widely used to validate fluid analysis (e.g., [4]). Two-dimensional flow fields given by random numbers are also widely used to validate fluid analysis.…”

Section: Introductionmentioning

confidence: 99%

“…The energy of this flow is analytically obtained to be constant under inviscid conditions. A spatial discretisation method with good conservation properties has been validated in previous studies using a two-dimensional inviscid field [4].…”

Section: Introductionmentioning

confidence: 99%

Non-linear response of kinetic energy in an inviscid Taylor-Green flow obtained by OpenFOAM-LES with respect to time increments

Ono,

Suzuki,

Kouchi

2024

Self Cite

This study investigates the conservation error of kinetic energy with respect to time increment using OpenFOAM LES. The energy conservation error is verified using an inviscid Taylor-Green vortex and the effect on energy conservation is checked by varying the time increment by a factor of 30. Differences in the response of turbulent energy conservation between large and small time increments are also verified. Higher order accuracy for time increments is expected when the kinetic energy conservation accuracy is high, however the actual behaviour in OpenFOAM needs to be investigated: as the implicit time integration method is used in OpenFOAM, a non-linear response is expected. As a result, it is evident that kinetic energy is not fully conserved in the inviscid flow of OpenFOAM. The kinetic energy distribution is similar for different time increments, with a different relationship between the conservation error observed in the range of large and small time increments.