The steady Navier–Stokes/energy system with temperature‐dependent viscosity—Part 2: The discrete problem and numerical experiments

Pérez, Carlos; Thomas, Jean-Marie; Blancher, Serge; Creff, R.

doi:10.1002/fld.1572

Cited by 28 publications

(22 citation statements)

References 30 publications

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“…Similar scenarios of numerical instability can arise in scalar advection‐diffusion systems 19 . Despite the numerous reports on backflow stabilization for flow problems 4,5,7‐16,20 and 2D heat mass transfer, 21‐25 these strategies have not been adopted for 3D cardiovascular scalar advection‐diffusion systems. Instead, to circumvent the numerical instability issues in the presence of backflow, mass transport models have resorted to unphysical approaches such as the imposition of arbitrary Dirichlet boundary conditions at the outlet faces, 26,27 artificial extensions of the computational domain 28 that seek to regularize the flow profile, or an artificial increase in the diffusivity of the scalar 29,30 .…”

Section: Introductionmentioning

confidence: 99%

Numerical considerations for advection‐diffusion problems in cardiovascular hemodynamics

Lynch

Nama

et al. 2020

Numer Methods Biomed Eng

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Numerical simulations of cardiovascular mass transport pose significant challenges due to the wide range of Péclet numbers and backflow at Neumann boundaries. In this paper we present and discuss several numerical tools to address these challenges in the context of a stabilized finite element computational framework. To overcome numerical instabilities when backflow occurs at Neumann boundaries, we propose an approach based on the prescription of the total flux. In addition, we introduce a “consistent flux” outflow boundary condition and demonstrate its superior performance over the traditional zero diffusive flux boundary condition. Lastly, we discuss discontinuity capturing (DC) stabilization techniques to address the well‐known oscillatory behavior of the solution near the concentration front in advection‐dominated flows. We present numerical examples in both idealized and patient‐specific geometries to demonstrate the efficacy of the proposed procedures. The three contributions discussed in this paper successfully address commonly found challenges when simulating mass transport processes in cardiovascular flows.

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Section: Introductionmentioning

confidence: 99%

Numerical considerations for advection‐diffusion problems in cardiovascular hemodynamics

Lynch

Nama

et al. 2020

Numer Methods Biomed Eng

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“…However, the results from do not cover the results in the present note since both contributions have different goals and use different analytical techniques. In addition, we like to mention that a finite element error analysis for a coupled system with temperature‐dependent viscosity is presented in .…”

Section: Introductionmentioning

confidence: 99%

Finite element methods for the incompressible Stokes equations with variable viscosity

2015

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ResumenPresenta los resultados de la comparación entre las ecuaciones de Stokes y de Navier-Stokes para la simulación del flujo de agua líquida, a condiciones atmosféricas, a través de una placa orificio concéntrica. A partir de los datos experimentales que fueron tomados en el banco de fluidos, se evaluaron las simulaciones de ambas ecuaciones, usando el software libre Freefem++cs, que se basa en el método de los elementos finitos; las variables evaluadas son velocidad y presión en un intervalo de tiempo. Al analizar los resultados obtenidos con las simulaciones y comparar con los datos experimentales se encontró que las ecuaciones de Navier-Stokes representan mejor el sistema que la ecuación de Stokes.Palabras clave: ecuaciones de Stokes y Navier-Stokes, modelo matemático, placa de orificio, simulación. AbstractThis paper presents the results of a comparison between Stokes and Navier-Stokes equations, in order to simulate the flow of liquid water at atmosferic conditions, through a concentric orifice plate. From experimental data taken from the fluids bank, the simulations of both equations were evaluated, using free software Freefem++CS, which

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“…We mention here only (Bernardi et al, 1995;Boland & Layton, 2 of 31 R. OYARZÚA, T. QIN, AND D. SCHÖTZAU 1990a,b;Cox et al, 2007;Farhloul & Zine, 2011;Pérez et al, 2008a,b;Tabata & Tagami, 2005) and the references therein. In particular, in (Pérez et al, 2008b) a conforming method is presented and analyzed for approximating non-isothermal incompressible fluid flow problems. However, the analysis there hinges on technical assumptions which may be difficult to verify in practice.…”

Section: Introductionmentioning

confidence: 99%

An exactly divergence-free finite element method for a generalized Boussinesq problem

Oyarzúa

Qin

Schötzau

2013

IMA Journal of Numerical Analysis

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We propose and analyze a mixed finite element method with exactly divergence-free velocities for the numerical simulation of a generalized Boussinesq problem, describing the motion of a non-isothermal incompressible fluid subject to a heat source. The method is based on using divergence-conforming elements of order k for the velocities, discontinuous elements of order k − 1 for the pressure, and standard continuous elements of order k for the discretization of the temperature. The H 1-conformity of the velocities is enforced by a discontinuous Galerkin approach. The resulting numerical scheme yields exactly divergence-free velocity approximations; thus, it is provably energy-stable without the need to modify the underlying differential equations. We prove the existence and stability of discrete solutions, and derive optimal error estimates in the mesh size for small and smooth solutions.

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The steady Navier–Stokes/energy system with temperature‐dependent viscosity—Part 2: The discrete problem and numerical experiments

Cited by 28 publications

References 30 publications

Numerical considerations for advection‐diffusion problems in cardiovascular hemodynamics

Numerical considerations for advection‐diffusion problems in cardiovascular hemodynamics

Finite element methods for the incompressible Stokes equations with variable viscosity

An exactly divergence-free finite element method for a generalized Boussinesq problem

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