Comparing vortex methods and finite difference methods in a homogeneous turbulent shear flow

Yokota, Rio; Obi, Shinnosuke

doi:10.1002/fld.2102

Cited by 5 publications

(7 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The vortex method uses the convergent core spreading method with reinitialization (31) . The shear-periodic boundary condition in the vortex method is calculated by an extension of the periodic FMM to handle shear (52) .…”

Section: Homogeneous Shear Turbulencementioning

confidence: 99%

“…Isosurface of II (Vortex Method) (52) They also investigated the suitable turbulence length scale that can be used to construct a dimensionless and universal shear-rate parameter, which can be used as an indicator of streaky structures for both the homogeneous shear flow and high shear regions near the wall. This dimensionless shear-rate parameter is defined as…”

Section: Journal Of Fluid Science and Technologymentioning

confidence: 99%

See 1 more Smart Citation

Vortex Methods for the Simulation of Turbulent Flows: Review

Yokota

Obi

2011

JFST

View full text Add to dashboard Cite

Vortex methods are a group of Lagrangian and semi-Lagrangian methods based on the vorticity-streamfunction or vorticity-velocity formulation of the Navier-Stokes equation, and provide an interesting alternative to grid based methods for external flows dominated by unsteady vortical motion. In the present review article, we will assess the advantages and disadvantages of vortex methods for the simulation of incompressible turbulent flows, based on the speed and accuracy benchmarks that have been performed recently. Our goal is to objectively and quantitatively evaluate the performance of this non-standard method, by directly comparing it's speed and accuracy against finite difference and pseudo-spectral DNS codes under identical calculation conditions. We also present examples of vortex methods in engineering applications of turbulent flows.

show abstract

Section: Homogeneous Shear Turbulencementioning

confidence: 99%

Section: Journal Of Fluid Science and Technologymentioning

confidence: 99%

Vortex Methods for the Simulation of Turbulent Flows: Review

Yokota

Obi

2011

JFST

View full text Add to dashboard Cite

show abstract

“…Fast algorithms have been also applied in combination with particle methods for the solution of problems with periodic boundary conditions [17,18] . For instance, Yokota and Barba, and Yokota and Obi employed the periodic FMM to study isotropic turbulence and homogeneous shear flows, respectively [19,20] . Sakajo and Okamoto [21] present an approach in which an exponential mapping transforms the periodic DVM function into a rational function.…”

Section: Introductionmentioning

confidence: 99%

Fast multipole method applied to Lagrangian simulations of vortical flows

Ricciardi

Wolf

Bimbato

2017

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

Lagrangian simulations of unsteady vortical flows are accelerated by the multi-level fast multipole method, FMM. The combination of the FMM algorithm with a discrete vortex method, DVM, is discussed for free domain and periodic problems with focus on implementation details to reduce numerical dissipation and avoid spurious solutions in unsteady inviscid flows. An assessment of the FMM-DVM accuracy is presented through a comparison with the direct calculation of the Biot-Savart law for the simulation of the temporal evolution of an aircraft wake in the Trefftz plane. The role of several parameters such as time step restriction, truncation of the FMM series expansion, number of particles in the wake discretization and machine precision is investigated and we show how to avoid spurious instabilities. The FMM-DVM is also applied to compute the evolution of a temporal shear layer with periodic boundary conditions. A novel approach is proposed to achieve accurate solutions in the periodic FMM. This approach avoids a spurious precession of the periodic shear layer and solutions are shown to converge to the direct Biot-Savart calculation using a cotangent function.

show abstract

“…Lindsay and Krasny [15] presented a divide and conquer methodology with an adaptive local refinement to accelerate the solution of vortex sheet motion. Yokota et al [25][26][27] employed the fast multipole method [10,17], FMM, to perform fast simulations of isotropic turbulence and homogeneous shear flows using vortex methods.…”

Section: Introductionmentioning

confidence: 99%

“…These authors studied several aspects of the problem including the regularization of the kernel and the development of instabilities in the solution. Fast algorithms such as the FMM have been applied in combination with vortex methods for the solution of flows with periodic boundary conditions [7,20,[25][26][27]. In general, periodicity is implemented in the FMM through replication of the multipole expansions of the computational domain.…”

Section: Introductionmentioning

confidence: 99%

A fast algorithm for simulation of periodic flows using discrete vortex particles

Ricciardi

Wolf

Bimbato

2017

J Braz. Soc. Mech. Sci. Eng.

View full text Add to dashboard Cite

We present a novel fast algorithm for flow simulations using the discrete vortex method, DVM, for problems with periodic boundary conditions. In the DVM, the solution of the velocity field induced by interactions among N discrete vortex particles is governed by the Biot-Savart law and, therefore, leads to a computational cost proportional to O(N 2). The proposed algorithm combines exponential and power series expansions implemented using a divide and conquer strategy to accelerate the calculation of the cotangent kernel that models periodic boundary conditions. The fast multipole method, FMM, is applied for the solution of singular terms appearing in the power series expansion and also for the exponential series expansion. Error and computational cost analyses are performed for the individual steps of the algorithm for double and quadruple machine precision. The current method presents more accurate solutions when compared to those obtained by periodic domain replication using the free-field FMM kernel. The novel algorithm provides computational savings of nearly 240 times for double-precision simulations with one million particles when compared to the direct calculation of the Biot-Savart law.

show abstract

Comparing vortex methods and finite difference methods in a homogeneous turbulent shear flow

Cited by 5 publications

References 20 publications

Vortex Methods for the Simulation of Turbulent Flows: Review

Vortex Methods for the Simulation of Turbulent Flows: Review

Fast multipole method applied to Lagrangian simulations of vortical flows

A fast algorithm for simulation of periodic flows using discrete vortex particles

Contact Info

Product

Resources

About