A least-squares finite element formulation for unsteady incompressible flows with improved velocity–pressure coupling

Pontaza, Juan P.

doi:10.1016/j.jcp.2006.01.013

Cited by 35 publications

(39 citation statements)

References 25 publications

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“…However, due to lack of velocity and pressure coupling, the least-squares formulation in its standard form is un-stable and results in a poor evolution (with spurious oscillations) of primary variables with time. To overcome this we introduce an iterative penalization scheme, on the similar lines of [18,34], for the transient pressure-velocity-stress first-order system of Navier-Stokes equations. By penalty method, we recast the constrained minimization problem into an unconstrained minimization problem through the use of the penalty method [14,44].…”

Section: A Least-squares Finite Element Model For Flows Of Viscous Inmentioning

confidence: 99%

“…The least-squares formulation allows for the construction of finite element models for fluids that, when combined with high-order finite element technology [22,4,5,38,17,29,31,31,49] possess many of the attractive qualities associated with the well-known Ritz method [43] such as global minimization, best approximation with respect to a well-defined norm, and symmetric positive-definiteness of the resulting finite element coefficient matrix [9]. However, the previous applications of the least-squares method, have often been plagued with spurious solution oscillations [34] and poor conservation of physical quantities (like dilatation, mass, volume) [16]. The least-squares formulation, when combined with high-order spectral/hp finite element technology, results in a better conservation of the physical quantities and reduces the instability and spurious oscillations of solution variables with time [18,34].…”

mentioning

confidence: 99%

“…However, the previous applications of the least-squares method, have often been plagued with spurious solution oscillations [34] and poor conservation of physical quantities (like dilatation, mass, volume) [16]. The least-squares formulation, when combined with high-order spectral/hp finite element technology, results in a better conservation of the physical quantities and reduces the instability and spurious oscillations of solution variables with time [18,34].…”

mentioning

confidence: 99%

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RETRACTED: Higher-order Spectral/hp Finite Element Technology for Shells and Flows of Viscous Incompressible Fluids

Vallala

Reddy

2013

MCA

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Abstract-This study deals with the use of high-order spectral/hp approximation functions in finite element models of various of nonlinear boundary-value and initial-value problems arising in the fields of structural mechanics and flows of viscous incompressible fluids. For many of these classes of problems, the high-order (typically, polynomial order 4  p ) spectral/hp finite element technology offers many computational advantages over traditional low-order (i.e., 3 < p ) finite elements. For instance, higher-order spectral/hp finite element procedures allow us to develop robust structural elements such as beams, plates, and shells in a purely displacement-based setting, which avoid all forms of numerical locking. For fluid flows, when combined with least-squares variational principles, the higher-order spectral/hp technology allows us to develop efficient finite element models that always yield a symmetric positive-definite (SPD) coefficient matrix and, hence, robust iterative solvers can be used. Also, the use of spectral/hp finite element technology results in a better conservation of physical quantities like dilatation, volume, and mass, and stable evolution of variables with time for transient flows. The present study considers the weak-form based displacement finite element models elastic shells and the least-squares finite element models of the Navier-Stokes equations governing flows of viscous incompressible fluids. Numerical solutions of several nontrivial benchmark problems are presented to illustrate the accuracy and robustness of the developed finite element technology.

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Section: A Least-squares Finite Element Model For Flows Of Viscous Inmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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RETRACTED: Higher-order Spectral/hp Finite Element Technology for Shells and Flows of Viscous Incompressible Fluids

Vallala

Reddy

2013

MCA

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“…Considerable effort has thus been placed on the development and evaluation of numerical methods for the solution to PB problems [10][11][12][13]. The least-squares method has been investigated and applied in the field of solid-and fluid mechanics [14][15][16][17][18][19][20][21][22]. However, in recent years the least-squares method has been adopted for the solution of chemical reactor problems, e.g.…”

Section: Introductionmentioning

confidence: 99%

Spectral solution of the breakage–coalescence population balance equation Picard and Newton iteration methods

Solsvik

Jakobsen

2016

Applied Mathematical Modelling

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The behavior of dispersed systems such as gas-liquids or liquid-liquid systems depends on the characteristics of the dispersed phase. The population balance (PB) equation is encountered in numerous engineering disciplines in order to describe complex processes where the accurate prediction of the dispersed phase plays a major role for the overall behavior of the system. In the present study, the orthogonal collocation, Galerkin and least-squares methods have been adopted to solve a non-linear PB equation which consists of both breakage and coalescence terms. The performance of the methods is demonstrated by comparing the numerical solution results with the (manufactured) analytical solution of the problem. For the least-squares method, the choice of linearization technique influences the numerical performance, whereas the Galerkin and orthogonal collocation methods obtain the same numerical accuracy for both the Picard and Newton iteration techniques. The least-squares method suffers from lack of convergency using the Picard method. On the other hand, if the Newton method is employed, the least-squares method obtains the same accuracy as the Galerkin and orthogonal collocation methods.

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“…In the last decades, the least-squares method has been applied to solve a variety of different problems, e.g., the Stokes equations [13][14][15][16], Euler equations [17], Navier-Stokes equations [18][19][20][21], electro-magnetism [22], viscoelastic flows [23], Burgers equation [24] and sound propagation [25,26]. The least-squares method is a novel numerical solution technique in the field of chemical reactor engineering.…”

Section: Introductionmentioning

confidence: 99%

On the solution of the advection equation and advective dominated reactor models by weighted residual methods

Solsvik

Jakobsen

2015

Computers & Fluids

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A least-squares finite element formulation for unsteady incompressible flows with improved velocity–pressure coupling

Cited by 35 publications

References 25 publications

RETRACTED: Higher-order Spectral/hp Finite Element Technology for Shells and Flows of Viscous Incompressible Fluids

RETRACTED: Higher-order Spectral/hp Finite Element Technology for Shells and Flows of Viscous Incompressible Fluids

Spectral solution of the breakage–coalescence population balance equation Picard and Newton iteration methods

On the solution of the advection equation and advective dominated reactor models by weighted residual methods

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