Dimitri Hatziavramidis

Chebyshev expansion methods for the solution of the extended graetz problem

Abstract The extended Graetz problem, a classical problem described by an equation with anon-self-adjoint second-order elliptic differential operator, is solved by two numerical methods based on Chebyshev expansions: A Chebyshev-finite difference method and a Chebyshev “finite” element method. The latter relies entirely on Chebyshev expansions; global in the bounded (radial) coordinate direction and local in the unbounded (axial) direction and proves to be more accurate than the Chebyshev-finite difference method in resolving singularities. Both methods can be applied to general type boundary-value problems involving second-order elliptic operators, have accuracy comparable to high order finite difference schemes and are operation cost efficient.

Solutions of the two-dimensional Navier-Stokes equations by Chebyshev expansion methods

Abstract The steady two-dimensional Navier-Stokes equations in both the vorticity-stream function and the vorticity-velocity formulation are solved by Chebyshev expansion methods. Numerical experiments for the driven flow in a rectangular cavity and the developing flow in a circular tube at low Reynolds numbers are described.

An integral Chebyshev expansion method for boundary-value problems of O.D.E. type

Abstract A Chebyshev expansion method for the solution of boundary-value problems of O.D.E. type is presented. The method employs the pseudospectral (collocation) approximation and generates approximations to the lower order derivatives of the function through successive integrations of the Chebyshev polynomial approximation to the highest order derivative. The method is easier to implement than spectral methods employing the Galerkin and tau approximations and yields results of comparable accuracy to these methods, with reduced computing requirements. Applications to the linear stability problems for plane Poiseuille and the Blasius boundary layer flows are presented.

Modeling and Design of jet pumps

Models for jet pumps currently are derived under the assumption that the power and well fluids are incompressible liquids that, in many cases, are assumed to have equal densities: When either the well or the power fluid contains gas, current design practices still use the equations for incompressible liquids and account for the presence of gas by modifying the mass-flow-rate ratio and the friction-loss coefficients. This paper proposes a new approach to modeling pumps operating under multiphase-flow conditions.

A pseudospectral method for the solution of the two-dimensional Navier-Stokes equations in the primitive variable formulation

Abstract A pseudospectral method was developed for the solution of the Navier-Stokes equations for incompressible flows in the primitive-variable formulation. The method employs Chebyshev expansion methods in order to generate approximations to the momentum and pressure equtions and utilizes a well-known fractional time-step procedure in obtaining a solution to these equations. Results for the buoyancy-driven flow in a square enclosure with nonisothermal vertical and insulated horizontal walls, at Rayleigh numbers in the range 1.4 × 10 4 –1.4 × 10 6 , are represented. The proposed method is easy to implement and can accurately reproduce the physics of the flow under consideration from transient to steady state.

Pseudospectral solutions of laminar heat transfer problems in pipelines

Abstract Problems of laminar heat transfer associated with pipeline transport of oil under laminar flow conditions are solved by a relatively new numerical technique. This technique accommodates for the peculiarity of the domain of solution (one dimension, the axial, even when it is non-dimensionalized, is far more extended than the other two) and exhibits remarkable features in terms of computational economy, stability and accuracy. The main interest in this paper is the adaptation of the method to problems with different boundary conditions approximating real pipelines (offshore, insulated, buried).

Concentration dependent translational self‐friction coefficient of rod‐like macromolecules in dilute suspensions

A general theory for the concentration dependent translational self‐friction coefficients of rod‐like macromolecules in suspensions is presented. Adopting the Kirkwood–Riseman model for the polymer and using a multiple scattering cluster expansion approach we have generated explicit expressions for the friction coefficients at infinite dilution as well as the leading terms of the concentration dependent friction coefficients for both theta solutions and solutions of hard rod‐like macromolecules. The leading terms of the concentration dependent friction coefficients in both cases show a weak dependence on the molecular weight of the polymer, a dependence which is absent from the corresponding coefficients for spheres and flexible polymer chains in solution.

A New Computational Approach to the Miscible Displacement Problem

Development of a 2D miscible computer code based on a pseudospectral method that uses Chebyshev expansions and a grid adaptative to the position of the front. The effect of physical dispersion is explicitely induced, while the effect of numerical dispersion is greatly suppressed. The code is shown to have exceptional convergence, accuracy, stability, and computational economy; it accurately predicts the position of the displacement front for 1D miscible and immiscible displacements. It also predicts oil recoveries and breakthrough times for 2D miscible displacements with unfavorable mobility ratios that are in agreement with experimental data and is shown to be effective in resolving details of viscous fingering phenomena.

The effective mobility of fine‐texture dispersions flowing in porous media

An effective medium theory for predicting the mobility of fine‐texture dispersions (i.e., foams and emulsions) flowing in porous media is presented. The dispersions are viewed as random arrays of mobile spheres of uniform radius, smaller than the pore radii, imbedded in a fluid of different mobility, and their flow is approximated as a diffusion‐limited process. Using a multiple scattering approach, analytic expressions for the mobility of the dispersion in terms of the ratio of the mobilities of the individual phases and the volumetric fraction of the dispersed phase are generated.