Analysis of a Decoupled Time-Stepping Scheme for Evolutionary Micropolar Fluid Flows

Ravindran, S. S.

doi:10.1155/2016/7010645

Cited by 5 publications

(7 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…in [10], [25], [12] and [11]. For the special subcase of micropolar fluids with p = 2 optimal convergence rates for strong solutions are proved in [41], [43]. The convergence of a fully discrete approximation towards a mollified problem for electrorheological fluids with variable exponents is proved in [15].…”

Section: Ad (Iii)mentioning

confidence: 94%

Analysis of fully discrete, quasi non-conforming approximations of evolution equations and applications

Berselli

Kaltenbach

Růžička

2021

Math. Models Methods Appl. Sci.

View full text Add to dashboard Cite

In this paper, we consider fully discrete approximations of abstract evolution equations, by means of a quasi non-conforming spatial approximation and finite differences in time (Rothe–Galerkin method). The main result is the convergence of the discrete solutions to a weak solution of the continuous problem. Hence, the result can be interpreted either as a justification of the numerical method or as an alternative way of constructing weak solutions. We set the problem in the very general and abstract setting of pseudo-monotone operators, which allows for a unified treatment of several evolution problems. The examples — which fit into our setting and which motivated our research — are problems describing the motion of incompressible fluids, since the quasi non-conforming approximation allows to handle problems with prescribed divergence. Our abstract results for pseudo-monotone operators allow to show convergence just by verifying a few natural assumptions on the operator time-by-time and on the discretization spaces. Hence, applications and extensions to several other evolution problems can be easily performed. The results of some numerical experiments are reported in the final section.

show abstract

Section: Ad (Iii)mentioning

confidence: 94%

Analysis of fully discrete, quasi non-conforming approximations of evolution equations and applications

Berselli

Kaltenbach

Růžička

2021

Math. Models Methods Appl. Sci.

View full text Add to dashboard Cite

show abstract

“…To decouple the velocity components and get a symmetric stiffness matrix for the velocity subproblems, we will treat convection explicitly, extrapolating

\left(\nabla \boldsymbol{u}\right)\boldsymbol{u}

. Moreover, to separate

\boldsymbol{\sigma}

and

\boldsymbol{u}

and even decouple all stress components, we discretize the constitutive equation (6) in time as done by Ravindran, 11 see Section 4.2.…”

Section: Weak Form and Time Discretizationmentioning

confidence: 99%

“…4,5 Therefore, it is of scientific interest to design methods that segregate the calculation of the unknowns. [6][7][8] Such decoupling schemes have lately become more common [9][10][11][12] and are currently the most effective way to enable large-scale viscoelastic flow simulations.…”

Section: Introductionmentioning

confidence: 99%

Consistent splitting schemes for incompressible viscoelastic flow problems

Pacheco

Castillo

2023

Numerical Meth Engineering

View full text Add to dashboard Cite

Viscoelastic fluids are highly challenging from the rheological standpoint, and their discretization demands robust, efficient numerical solvers. Simulating viscoelastic flows requires combining the Navier–Stokes system with a dynamic tensorial equation, increasing mathematical and computational demands. Hence, fractional‐step methods decoupling the calculation of the flow quantities are an attractive option. In consistent fractional‐step schemes, the splitting of the equations is derived from the continuous level, so that neither mass nor momentum balance is sacrificed. Thus, no corrections or velocity projections are needed, resulting in fewer algorithmic steps than other classical approaches. Moreover, consistency guarantees the absence of both numerical boundary layers and splitting errors, enabling high‐order accuracy in space and time. This article introduces the first consistent splitting methods for incompressible flows of viscoelastic fluids, for which arbitrary constitutive laws are allowed. We present the formulation and the algorithm, along with various numerical examples testing their accuracy. First‐, second‐ and third‐order backward‐differentiation schemes are numerically tested, and optimal convergence is confirmed for several spatial and temporal discretizations. Furthermore, good numerical stability is verified in challenging benchmark problems, including steady and time‐dependent solutions.

show abstract

“…X is the vector consisting of the nodal values of the velocity and pressure. A second-order backward differentiation formula (BDF2) [29,30] is applied for the temporal discretization of Eq. (2.12), as shown in Eq.…”

Section: Discrtizationmentioning

confidence: 99%

A Parallel Numerical Method for Risk Assessment of Myocardial Infarction During Liver Transplantation: A Case Study

Yan¹,

Shang²,

Li³

et al. 2022

AAMM

View full text Add to dashboard Cite

Coronary artery disease is a devastating complication of some patients undergoing liver transplantation. Anesthesia, anhepatic blood flow occlusion, and reperfusion of the liver can cause severe fluctuations in hemodynamics. However, the vast majority of liver transplant patients cannot undergo invasive coronary examinations due to their critical illness and abnormal coagulation function. In this paper, we present a retrospective case of acute myocardial infarction during surgery in order to demonstrate a noninvasive method to obtain coronary hemodynamic functional information based on scalable computational fluid dynamics technology. A P 1 −P 1 stabilized finite element method and second-order backward differentiation formula are applied to discretize the time-dependent Navier-Stokes equations in the spatial and temporal directions, respectively. A Windkessel model constructed based on the measured clinic data is used to characterize the outlet blood flow. We then apply a parallel Newton-Krylov method with a restricted additive Schwarz preconditioner to accelerate the timeliness of the simulation. The simulated functional indicator successfully verifies the myocardial ischemia in the anhepatic phase of liver transplantation. We also present the parallel performance of the algorithm on a supercomputer, and the results show that the proposed solver achieves over 55% parallel efficiency with 3840 processor cores.

show abstract

Analysis of a Decoupled Time-Stepping Scheme for Evolutionary Micropolar Fluid Flows

Cited by 5 publications

References 29 publications

Analysis of fully discrete, quasi non-conforming approximations of evolution equations and applications

Analysis of fully discrete, quasi non-conforming approximations of evolution equations and applications

Consistent splitting schemes for incompressible viscoelastic flow problems

A Parallel Numerical Method for Risk Assessment of Myocardial Infarction During Liver Transplantation: A Case Study

Contact Info

Product

Resources

About