Kinetically reduced local Navier-Stokes equations for simulation of incompressible viscous flows

Borok, Sofia; Ansumali, Santosh; Karlin, Iliya V.

doi:10.1103/physreve.76.066704

Cited by 30 publications

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References 20 publications

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“…These share a theme of locality of data access, yielding better parallel computing efficiency. Similarly, pseudocompressibility methods for fluid flow are potentially better for distributed computing [13,14].…”

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confidence: 99%

Delayed Difference Scheme for Large Scale Scientific Simulations

2014

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We argue that the current heterogeneous computing environment mimics a complex nonlinear system which needs to borrow the concept of time-scale separation and the delayed difference approach from statistical mechanics and nonlinear dynamics. We show that by replacing the usual difference equations approach by a delayed difference equations approach, the sequential fraction of many scientific computing algorithms can be substantially reduced. We also provide a comprehensive theoretical analysis to establish that the error and stability of our scheme is of the same order as existing schemes for a large, well-characterized class of problems.

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confidence: 99%

Delayed Difference Scheme for Large Scale Scientific Simulations

2014

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“…The Entropically Damped Artificially Compressible (EDAC) method of Clausen [13,14] is an alternative to the artificial compressibility used by the weakly-compressible formulation. This method is similar to the kinetically reduced local Navier-Stokes method presented in [15,16,17]. However, the EDAC scheme uses the pressure instead of the grand potential as the thermodynamic variable and this simplifies the resulting equations.…”

Section: Introductionmentioning

confidence: 99%

Entropically damped artificial compressibility for SPH

Ramachandran

Puri

2019

Computers & Fluids

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In this paper, the Entropically Damped Artificial Compressibility (EDAC) formulation of Clausen (2013) is used in the context of the Smoothed Particle Hydrodynamics (SPH) method for the simulation of incompressible fluids. Traditionally, weakly-compressible SPH (WCSPH) formulations have employed artificial compressiblity to simulate incompressible fluids. EDAC is an alternative to the artificial compressiblity scheme wherein a pressure evolution equation is solved in lieu of coupling the fluid density to the pressure by an equation of state. The method is explicit and is easy to incorporate into existing SPH solvers using the WCSPH formulation. This is demonstrated by coupling the EDAC scheme with the recently proposed Transport Velocity Formulation (TVF) of Adami et al. (2013). The method works for both internal flows and for flows with a free surface. Several benchmark problems are considered to evaluate the proposed scheme and it is found that the EDAC scheme gives results that are as good or sometimes better than those produced by the TVF or standard WCSPH. The scheme is robust and produces smooth pressure distributions and does not require the use of an artificial viscosity in the momentum equation although using some artificial viscosity is beneficial.

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“…Many of the physical phenomena in fluid mechanics are formulated according to the unsteady viscous incompressible Navier-Stokes (INS) equations, which has the nondimensional formula consisting of the momentum equations and the continuity equation [1][2][3][4][5][6][7][8] u + (u ⋅ ∇) u + ∇ = 1 ∇ 2 u,…”

Section: Introductionmentioning

confidence: 99%

“…The KRLNS equations are proposed for the simulation of low Mach number flows in [2], and used the spectral element method to find the numerical solution of the three-dimensional Taylor Green vortex flow. In [3], two-dimensional KRLNS system is simplified and compared with a Chorin's artificial compressibility method for steady state computation of the flow in a lid-driven cavity at various Reynolds numbers, the Taylor Green vortex flow is demonstrated that the KRLNS equations correctly describe the time evolution of the velocity and of the pressure, for this purpose, the explicit Mac Cormack scheme is used. In [5] the KRLNS equations are applied to two-dimensional simulation of doubly periodic shear layers and decaying homogeneous isotropic turbulence, to solve these equations have been used the central difference scheme for the spatial discretization in both advection and diffusion terms and four stages Runge-Kutta method for the time integration, the numerical results are compared with those obtained by the artificial compressibility method, the lattice Boltzmann method, and the pseudospectral method.…”

Section: Introductionmentioning

confidence: 99%

A New Approximate Analytical Solutions for Two- and Three-Dimensional Unsteady Viscous Incompressible Flows by Using the Kinetically Reduced Local Navier-Stokes Equations

Al‐Saif

Harfash

2019

Journal of Applied Mathematics

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In this work, the kinetically reduced local Navier-Stokes equations are applied to the simulation of two- and three-dimensional unsteady viscous incompressible flow problems. The reduced differential transform method is used to find the new approximate analytical solutions of these flow problems. The new technique has been tested by using four selected multidimensional unsteady flow problems: two- and three-dimensional Taylor decaying vortices flow, Kovasznay flow, and three-dimensional Beltrami flow. The convergence analysis was discussed for this approach. The numerical results obtained by this approach are compared with other results that are available in previous works. Our results show that this method is efficient to provide new approximate analytic solutions. Moreover, we found that it has highly precise solutions with good convergence, less time consuming, being easily implemented for high Reynolds numbers, and low Mach numbers.

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Kinetically reduced local Navier-Stokes equations for simulation of incompressible viscous flows

Cited by 30 publications

References 20 publications

Delayed Difference Scheme for Large Scale Scientific Simulations

Delayed Difference Scheme for Large Scale Scientific Simulations

Entropically damped artificial compressibility for SPH

A New Approximate Analytical Solutions for Two- and Three-Dimensional Unsteady Viscous Incompressible Flows by Using the Kinetically Reduced Local Navier-Stokes Equations

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