Residence time in a semi-enclosed domain from the solution of an adjoint problem

Delhez, Eric; Heemink, A.W.; Deleersnijder, Éric

doi:10.1016/j.ecss.2004.07.013

Cited by 148 publications

(129 citation statements)

References 19 publications

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“…The TTD is then given by the flux of adjoint Green's function leaving the domain through the surface. Delhez et al (2004) explain a similar method to compute the residence time, which is closely related to the TTD. This approach requires that the adjoint advection-diffusion system be integrated, not the forward system.…”

Section: Unsteady Flowmentioning

confidence: 99%

On transit-time distributions in unsteady circulation models

et al. 2008

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Section: Unsteady Flowmentioning

confidence: 99%

On transit-time distributions in unsteady circulation models

et al. 2008

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“…This result is identical to the definition of flushing time that has applications in environmental flows. 24,25 Note that this measure of RT does not require solving the advectiondiffusion problem and can be directly calculated from the velocity field at the boundaries of the region of interest, i.e., all u(x, t) such that x ∈ ∂ τ . Since the incompressibility assumption was used to derive Eq.…”

Section: A Residence Time Calculationmentioning

confidence: 99%

A non-discrete method for computation of residence time in fluid mechanics simulations

2013

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Cardiovascular simulations provide a promising means to predict risk of thrombosis in grafts, devices, and surgical anatomies in adult and pediatric patients. Although the pathways for platelet activation and clot formation are not yet fully understood, recent findings suggest that thrombosis risk is increased in regions of flow recirculation and high residence time (RT). Current approaches for calculating RT are typically based on releasing a finite number of Lagrangian particles into the flow field and calculating RT by tracking their positions. However, special care must be taken to achieve temporal and spatial convergence, often requiring repeated simulations. In this work, we introduce a non-discrete method in which RT is calculated in an Eulerian framework using the advection-diffusion equation. We first present the formulation for calculating residence time in a given region of interest using two alternate definitions. The physical significance and sensitivity of the two measures of RT are discussed and their mathematical relation is established. An extension to a point-wise value is also presented. The methods presented here are then applied in a 2D cavity and two representative clinical scenarios, involving shunt placement for single ventricle heart defects and Kawasaki disease. In the second case study, we explored the relationship between RT and wall shear stress, a parameter of particular importance in cardiovascular disease. C 2013 AIP Publishing LLC. [http://dx

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“…In general, the analytical solution of the direct problem (1) cannot be found; however, the residence time of a tracer can be obtained (Delhez et al, 2004;Deleersnijder et al, 2006a,b). The residence time of a water or tracer parcel in a control domain is usually defined as the time taken by this parcel to leave the domain of interest (Bolin and Rodhe, 1973;Zimmerman, 1976 1988; Braunschweig et al, 2003;Takeoka, 1984;Delhez and Deleersnijder, 2006).…”

Section: Illustrationsmentioning

confidence: 99%

“…Mathematically, the mean residence time θ(x) of the tracer of initial mass m(t 0 ) released at time t 0 can be computed by monitoring the temporal evolution of the mass of the tracer in the control region (Bolin and Rodhe (1973); Takeoka (1984)) Delhez et al (2004) introduced an alternative procedure designed for numerical models. They showed that the residence time can be found from the solution of the adjoint problem to the advection-diffusion equation.…”

Section: Illustrationsmentioning

confidence: 99%

The backward Îto method for the Lagrangian simulation of transport processes with large space variations of the diffusivity

Spivakovskaya

Heemink²,

Deleersnijder³

2007

Ocean Sci.

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Abstract. Random walk models are a powerful tool for the investigation of transport processes in turbulent flows. However, standard random walk methods are applicable only when the flow velocities and diffusivity are sufficiently smooth functions. In practice there are some regions where the rapid but continuous change in diffusivity may be represented by a discontinuity. The random walk model based on backwardÎto calculus can be used for these problems. This model was proposed by LaBolle et al. (2000). The latter is best suited to the problems under consideration. It is then applied to two test cases with discontinuous diffusivity, highlighting the advantages of this method.

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Residence time in a semi-enclosed domain from the solution of an adjoint problem

Cited by 148 publications

References 19 publications

On transit-time distributions in unsteady circulation models

On transit-time distributions in unsteady circulation models

A non-discrete method for computation of residence time in fluid mechanics simulations

The backward Îto method for the Lagrangian simulation of transport processes with large space variations of the diffusivity

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