A. Segal

A mass‐conserving Level‐Set method for modelling of multi‐phase flows

A mass-conserving Level-Set method to model bubbly flows is presented. The method can handle high density-ratio flows with complex interface topologies, such as flows with simultaneous occurrence of bubbles and droplets. Aspects taken into account are: a sharp front (density changes abruptly), arbitrarily shaped interfaces, surface tension, buoyancy and coalescence of droplets/bubbles. Attention is paid to mass-conservation and integrity of the interface. The proposed computational method is a Level-Set method, where a Volume-of-Fluid function is used to conserve mass when the interface is advected. The aim of the method is to combine the advantages of the Level-Set and Volume-of-Fluid methods without the disadvantages. The flow is computed with a pressure correction method with the Marker-and-Cell scheme. Interface conditions are satisfied by means of the continuous surface force methodology and the jump in the density field is maintained similar to the ghost fluid method for incompressible flows

A Computational Model of the Electromagnetic Heating of Biological Tissue with Application to Hyperthermic Cancer Therapy

To investigate the potentialities of hyperthermia as a cancer therapy, computer simulations have been performed. This simulation consists of two tuccessive steps. First, the heat generated in a distribution of biological tissue when irradiated by a source of electromagnetic radiation is computed. The mathematical tool for determining the disbution of generated heat is the domain-integral-equation technique. This technique enables us to determine in a body with arbitrary distribution of permittivity and conductivity the electromagnetic field due to prescribed sources. The integral equation is solved numerically by an iterative minimization of the integrated square error. From the computed distribution of generated heat, the temperature distribution follows by solving numerically the pertaining heat transfer problem. The relevant differential equation together with initial and boundary conditions is solved numerically using a finite-element technique in space and a finite-difference technique in time. Numerical results pertaining to the temperature distribution in a model of the human pelvis are presented.

A theoretical model for core-annular flow of a very viscous oil core and a water annulus through a horizontal pipe

Abstract A theoretical model has been developed for core-annular flow of a very viscous oil core and a water annulus through a horizontal pipe. Special attention was paid to understanding how the buoyancy force on the core, resulting from any density difference between the oil and water, is counterbalanced. This problem was simplified by assuming the oil viscosity to be so high that any flow inside the core may be neglected and hence that there is no variation of the profile of the oil-water interface with time. In the model the core is assumed to be solid and the interface to be a solid/liquid interface. By means of the hydrodynamic lubrication theory it has been shown that the ripples on the interface moving with respect to the pipe wall can generate pressure variations in the annular layer. These result in a force acting perpendicularly on the core, which can counterbalance the buoyancy effect. To check the validity of the model, oil-water core-annular flow experiments have been carried out in a 5.08 cm and an 20.32-cm pipeline. Pressure drops measured have been compared with those calculated with the aid of the model. The agreement is satisfactory.

A numerical analysis of steady flow in a three-dimensional model of the carotid artery bifurcation

A finite element approximation of steady flow in a rigid three-dimensional model of the carotid artery bifurcation is presented. A Reynolds number of 640 and a flow division ratio of about 50/50, simulating systolic flow, was used. To limit the CPU- and I/O-times needed for solving the systems of equations, a mesh-generator was developed, which gives full control over the number of elements into which the bifurcation is divided. A mini-supercomputer, based on parallel and vector processing techniques, was used to solve the system of equations. The numerical results of axial and secondary flow compare favorably with those obtained from previously performed laser-Doppler velocity measurements. Also, the influence of the Reynolds number, the flow division ratio, and the bifurcation angle on axial and secondary flow in the carotid sinus were studied in the three-dimensional model. The influence of the interventions is limited to a relatively small variation in the region with reversed axial flow, more or less pronounced C-shaped axial velocity contours, and increasing or decreasing axial velocity maxima.

Finite-element-based computational methods for cardiovascular fluid-structure interaction

In this paper a combined arbitrary Lagrange-Euler fictitious domain (ALE-FD) method for fluid-structure interaction problems in cardiovascular biomechanics is derived in terms of a weighted residual finite-element formulation. For both fluid flow of blood and solid mechanics of vascular tissue, the performance of tetrahedral and hexahedral Crouzeix-Raviart elements are evaluated. Comparable convergence results are found, although for the test cases considered the hexahedral elements are more accurate. The possibilities that are offered by the ALE-FD method are illustrated by means of a simulation of valve dynamics in a simplified left ventricular flow model.

Aspects of Numerical Methods for Elliptic Singular Perturbation Problems

Upwind difference, defect correction and central difference schemes for the solution of the convection-diffusion equation with small viscosity coefficient are compared. It is shown that central difference schemes and hence also standard Galerkin finite element methods are preferable above upwind and defect correction schemes, when Gaussian elimination is used for the solution of the resulting system of equations.When iterative solution methods are employed good results can be achieved by a defect-correction method, whereas upwind difference schemes are generally inaccurate.

The Isnas Incompressible Navier-Stokes Solver - Invariant Discretization

The ISNaS-project aims at providing tools for computer aided design and engineering in aerodynamics and hydrodynamics by developing an Information System for the simulation of complex flows based on the Navier-Stokes equations. Major components of the project are the development of a method-shell and of accurate as well as robust solvers for both compressible and incompressible flows. For the incompressible case, guided by typical applications in the field of river and coastal hydrodynamics, a solution procedure is being developed that is capable of handling complicated geometries, including free surface effects, in particular for high-Reynolds number flow regimes. In the present paper the invariant discretization of the incompressible Navier-Stokes equations in general boundary-fitted coordinate systems is discussed. It is found to be important that certain rules are followed concerning the choice of unknowns and the approximation of the geometric quantities. This is illustrated by some preliminary results. Extensions to moving coordinate systems and time-varying computational grids are indicated.

Invariant discretization of the - model in general co-ordinates for prediction of turbulent flow in complicated geometries

Abstract An invariant formulation and finite volume discretization of the standard k-ϵ turbulence model in general curvilinear co-ordinates is presented. The k-ϵ model is implemented together with the incompressible Navier-Stokes equations on staggered grids with contravariant flux components as unknowns. A proof that k and ϵ are non-negative is given. Positive schemes in the implementation of the k-ϵ model are evaluated. Discretization of boundary conditions is considered. The numerical method is applied to a turbulent flow across a staggered tube bank.

A superlinearly convergent Mach-uniform finite volume method for the Euler equations on staggered unstructured grids

A Mach-uniform finite volume scheme for solving the unsteady Euler equations on staggered unstructured triangular grids that uses linear reconstruction is described. The scheme is applied to three benchmark problems and is found to be considerably more accurate than a similar scheme based on piecewise constant reconstruction.

Conservation properties of a new unstructured staggered scheme

Abstract In Wenneker et al. [Computation of compressible flows on unstructured staggered grids. In: Onate E, Bugeda G, Suarez B, editors. Proceedings European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000, Barcelona, 11–14 September 2000, Barcelona, 2000. CIMNE. http://ta.twi.tudelft.nl/users/wesseling/pub.html ] an unstructured staggered scheme for the two-dimensional (2D) Euler equations is discussed. Such a scheme cannot be in classic conservation form for momentum. The aim of the present paper is to formulate a generalized conservation form for momentum on unstructured staggered grids, and to demonstrate by numerical experiments that the scheme satisfies the Rankine–Hugoniot conditions. Numerical results for 1D Riemann problems on 2D unstructured grids confirm that the scheme converges to the entropy solution. In addition, transonic flow around an airfoil is computed.