Book Review: Computational Fluid Mechanics and Heat Transfer, by Dale A. Anderson

Shang, J. S.

doi:10.2514/3.48657

Cited by 55 publications

(105 citation statements)

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“…Continuum models are very commonly used, but are based on the assumption that the differential equation is valid at every point in space. The radially symmetric, compartmentbased, model only assumes that the differential equation is valid in an integral-averaged sense (and is, in effect, a finite volume discretization of the continuum model [34], an integration of the continuum model over volumes chosen to be on the scale of the biological cells), leading to a very natural framework for simulating mass balance processes. The compartmental model is limited to radially symmetric problems (cords, multicell spheroids), but this is a common constraint imposed in computational modelling for (i) efficiency of computation and (ii) direct comparison with mathematical analysis, which is often limited to such quasi-one-dimensional geometries.…”

Section: Discussionmentioning

confidence: 99%

Mathematical and computational models of drug transport in tumours

Groh

Hubbard

Jones

et al. 2014

J. R. Soc. Interface.

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The ability to predict how far a drug will penetrate into the tumour microenvironment within its pharmacokinetic (PK) lifespan would provide valuable information about therapeutic response. As the PK profile is directly related to the route and schedule of drug administration, an in silico tool that can predict the drug administration schedule that results in optimal drug delivery to tumours would streamline clinical trial design. This paper investigates the application of mathematical and computational modelling techniques to help improve our understanding of the fundamental mechanisms underlying drug delivery, and compares the performance of a simple model with more complex approaches. Three models of drug transport are developed, all based on the same drug binding model and parametrized by bespoke in vitro experiments. Their predictions, compared for a 'tumour cord' geometry, are qualitatively and quantitatively similar. We assess the effect of varying the PK profile of the supplied drug, and the binding affinity of the drug to tumour cells, on the concentration of drug reaching cells and the accumulated exposure of cells to drug at arbitrary distances from a supplying blood vessel. This is a contribution towards developing a useful drug transport modelling tool for informing strategies for the treatment of tumour cells which are 'pharmacokinetically resistant' to chemotherapeutic strategies.

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Section: Discussionmentioning

confidence: 99%

Mathematical and computational models of drug transport in tumours

Groh

Hubbard

Jones

et al. 2014

J. R. Soc. Interface.

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“…Alternative numerical advection algorithms can be found in Holt (1984); LeVeque (1990); Tannehill et al (1997). Another alternate is the flux-corrected transport algorithm of Boris & Book (1964), which is an Eulerian method based on Lagrangian considerations.…”

Section: Discussionmentioning

confidence: 99%

“…In the case of scalar advection of a tracer field, the concentration must always remain non-negative. Without proper handling of advection terms, numerical solutions can go unconditionally unstable, producing negative concentrations or spurious wiggles (Tannehill et al, 1997;Press et al, 1997). Historically, the first alternative was the unconditionally stable method of characteristics introduced by Courant et al (1952) (sometimes referred to as the CIR scheme; see LeVeque (1990)).…”

Section: Discretizationmentioning

confidence: 99%

“…We have chosen a multigrid method (Hackbusch, 1985;Briggs, 1987;Press et al, 1997;Tannehill et al, 1997). In order to solve (29) we need to evaluate the quantities F i,j and P i,j , as described in the following subsections.…”

Section: Discretizationmentioning

confidence: 99%

“…One way of avoiding such a problem is to solve first for the velocity vector potential A and then compute the velocity as ∇ × A. Although this approach has some advantages, much of its attractiveness is lost when applied to three-dimensional flow (Tannehill et al, 1997). Moreover, there are complications in implementing the pressure boundary condition in the vector potential formulation.…”

Section: Computation Of the Pressure Fieldmentioning

confidence: 99%

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Energy-Conserving Simulation of Incompressible Electro-Osmotic and Pressure-Driven Flow

Alam

Bowman

2002

Theoretical and Computational Fluid Dynamics

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Abstract.A numerical model for electro-osmotic flow is described. The advecting velocity field is computed by solving the incompressible Navier-Stokes equation. The method uses a semi-implicit multigrid algorithm to compute the divergence-free velocity at each grid point. The finite differences are second-order accurate and centered in space; however, the traditional second-order compact finite differencing of the Poisson equation for the pressure field is shown not to conserve energy in the inviscid limit. We have designed a non-compact finite differencing for the Laplacian in the pressure equation that allows exact energy conservation and affords second-order accuracy. The model also incorporates a new numerical method for passive scalar advection, called parcel advection, which accurately predicts the evolution of a passively traveling scalar pulse without requiring the addition of any artificial diffusion. The algorithm is used to confirm the experimentally observed asymmetric concentration profile that arises when an external pressure drop is imposed on electro-osmotic flow.

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Numerical method for the solution of non-linear two-dimensional inverse heat conduction problem using unstructured meshes

Duda

Taler

2000

Int. J. Numer. Meth. Engng.

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SUMMARYA new method of solving multidimensional heat conduction problems is formulated. The developed space marching method allows to determine quickly and exactly unsteady temperature distributions in the construction elements of irregular geometry. The method which is based on temperature measurements at the outer surface, is especially appropriate for determining transient temperature distribution in thick-wall pressure components. Two examples are included to demonstrate the capabilities of the new approach.

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Book Review: Computational Fluid Mechanics and Heat Transfer, by Dale A. Anderson

Cited by 55 publications

References 0 publications

Mathematical and computational models of drug transport in tumours

Mathematical and computational models of drug transport in tumours

Energy-Conserving Simulation of Incompressible Electro-Osmotic and Pressure-Driven Flow

Numerical method for the solution of non-linear two-dimensional inverse heat conduction problem using unstructured meshes

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