An artificial compressibility based fractional step method for solving time dependent incompressible flow equations. Temporal accuracy and similarity with a monolithic method

Nithiarasu, Perumal; Bevan, Rhodri L. T.; Murali, K.

doi:10.1007/s00466-012-0719-5

Cited by 9 publications

(5 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Nithiarasu [33,34] developed a fully-explicit CB split FE method, known as the CBS-AC scheme, which takes advantage of both standard AC and velocity correction approaches. Nithiarasu et al [35][36][37][38] further extended the fullyexplicit and semi-implicit versions of the CBS scheme to different applications as a unified approach to fluid dynamics problems [36]. In the present work, the proposed FSAC-PP unified solution concept for incompressible flows is different from the previous works.…”

Section: Introductionmentioning

confidence: 85%

A Unified Fractional-Step, Artificial Compressibility and Pressure-Projection Formulation for Solving the Incompressible Navier-Stokes Equations

Könözsy

Drikakis

2014

Commun. comput. phys.

View full text Add to dashboard Cite

This paper introduces a unified concept and algorithm for the fractional-step (FS), artificial compressibility (AC) and pressure-projection (PP) methods for solving the incompressible Navier-Stokes equations. The proposed FSAC-PP approach falls into the group of pseudo-time splitting high-resolution methods incorporating the characteristics-based (CB) Godunov-type treatment of convective terms with PP methods. Due to the fact that the CB Godunov-type methods are applicable directly to the hyperbolic AC formulation and not to the elliptical FS-PP (split) methods, thus the straightforward coupling of CB Godunov-type schemes with PP methods is not possible. Therefore, the proposed FSAC-PP approach unifies the fully-explicit AC and semi-implicit FS-PP methods of Chorin including a PP step in the dual-time stepping procedure to a) overcome the numerical stiffness of the classical AC approach at (very) low and moderate Reynolds numbers, b) incorporate the accuracy and convergence properties of CB Godunov-type schemes with PP methods, and c) further improve the stability and efficiency of the AC method for steady and unsteady flow problems. The FSAC-PPmethod has also been coupled with a non-linear, full-multigrid and fullapproximation storage (FMG-FAS) technique to further increase the efficiency of the solution. For validating the proposed FSAC-PP method, computational examples are presented for benchmark problems. The overall results show that the unified FSAC-PP approach is an efficient algorithm for solving incompressible flow problems.

show abstract

Section: Introductionmentioning

confidence: 85%

A Unified Fractional-Step, Artificial Compressibility and Pressure-Projection Formulation for Solving the Incompressible Navier-Stokes Equations

Könözsy

Drikakis

2014

Commun. comput. phys.

View full text Add to dashboard Cite

show abstract

“…In the scientific literature, the true transient term is usually discretized in order to obtain a second order of approximation. Increased accuracy deriving from a higher order of approximation has been proved (Nithiarasu et al, 2013), and it is used here to get benchmark quality results.…”

Section: Transient Natural Convectionmentioning

confidence: 99%

New benchmark solutions for transient natural convection in partially porous annuli

Massarotti

Ciccolella

Cortellessa

et al. 2016

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

View full text Add to dashboard Cite

Purpose - The purpose of this paper is to focus on the numerical analysis of transient free convection heat transfer in partially porous cylindrical domains. The authors analyze the dependence of velocity and temperature fields on the geometry, by analyzing transient flow behavior for different values of cavity aspect ratio and radii ratio; both inner and outer radius are assumed variable in order to not change the difference ro -ri . Moreover, several Darcy numbers have been considered. Design/methodology/approach - A dual time-stepping procedure based on the transient artificial compressibility version of the characteristic-based split algorithm has been adopted in order to solve the transient equations of the generalized model for heat and fluid flow through porous media. The present model has been validated against experimental data available in the scientific literature for two different problems, steady-state free convection in a porous annulus and transient natural convection in a porous cylinder, showing an excellent agreement. Findings - For vertically divided half porous cavities, with Rayleigh numbers equal to 3.4 ? 106 for the 4:1 cavity and 3.4 ? 105 for the 8:1 cavity, the numerical results show that transient oscillations tend to disappear in presence of cylindrical geometry, differently from what happens for rectangular one. The magnitude of this phenomenon increases with radii ratio; the porous layer also affects the stability of velocity and temperature fields, as oscillations tend to decrease in presence of a porous matrix with lower value of the Darcy number. Research limitations/implications - A proper analysis of partially porous annular cavities is fundamental for the correct estimation of Nusselt numbers, as the formulas provided for rectangular domains are not able to describe these problems. Practical implications - The proposed model represents a useful tool for the study of transient natural convection problems in porous and partially porous cylindrical and annular cavities, typical of many engineering applications. Moreover, a fully explicit scheme reduces the computational costs and ensures flexibility. Originality/value - This is the first time that a fully explicit finite element scheme is employed for the solution of transient natural convection in partially porous tall annular cavities

show abstract

“…For transient problems however Split B with additional pressure stability or Split A with dual time stepping may give a slightly better result [83,87,93]. (3.21); in the second we retain in that equation the pressure gradient corresponding to the beginning of the step, i.e., ∂ p n /∂ x i .…”

Section: The Split: Temporal Discretizationmentioning

confidence: 99%

The Characteristic-Based Split (CBS) Algorithm: A General Procedure for Compressible and Incompressible Flow

Zienkiewicz¹,

Taylor²,

Nithiarasu³

2014

The Finite Element Method for Fluid Dynamics

Self Cite

View full text Add to dashboard Cite

An artificial compressibility based fractional step method for solving time dependent incompressible flow equations. Temporal accuracy and similarity with a monolithic method

Cited by 9 publications

References 10 publications

A Unified Fractional-Step, Artificial Compressibility and Pressure-Projection Formulation for Solving the Incompressible Navier-Stokes Equations

A Unified Fractional-Step, Artificial Compressibility and Pressure-Projection Formulation for Solving the Incompressible Navier-Stokes Equations

New benchmark solutions for transient natural convection in partially porous annuli

The Characteristic-Based Split (CBS) Algorithm: A General Procedure for Compressible and Incompressible Flow

Contact Info

Product

Resources

About