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Master of Science in Engineering Mathematics

Bassem's MSc in Eng. Math. Summary

Thesis

July 2007

Cairo University

Engineering Mathematics and Physics Department

Thesis Title: Flowfield Dependent Variation Method Applied to Compressible Euler Flow Equations (PDF)

Abstract

Many practical CFD problems in industry and research attain crucial physical situations. In the recent decades all CFD research efforts were directed towards the development of numerical techniques that are able to solve these situations accurately. To accurately predict flow properties the solution technique should be able to handle the interactions between high/low speeds, compressible/incompressible, subsonic/transonic/supersonic flows.

The present thesis aims at developing time accurate flow solver for Euler equations. This solver should be able to operate on different flow regimes seamlessly. The capabilities of the flowfield-dependent mixed explicit/implicit scheme, also known as flowfield dependent variation (FDV) method, have been investigated. Finite element techniques have been used to discretize the flow domain via standard Galerkin method. Several benchmarks have been tested. These test cases have been selected to clarify the ability of the FDV method to resemble complex flow situations and to cover a wide range of flow regimes. Good agreement with published literature has been obtained in all cases.

Advisor

Prof. Adel A. Megahed


Design simulation









Publications

Teaching Experiences

Engineering Mathematics and Physics Dept.,

Cairo University

Mechanics 1.A:

  • Vector algebra and its application to solid geometry
  • Force and resultant of a system of forces in space
  • Moments of forces and couples
  • The equivalent force - couple systems the wrench
  • Equilibrium of particles and rigid body subjected to:
    • Coplanar forces
    • System of three-dimensional forces and couples

Mechanics 1.B:

  • Kinematics of a particle: Displacement, velocity and acceleration of particle in Cartesian, intrinsic and polar coordinates. Applications on rectilinear and curvilinear motion
  • Kinetics of a particle: Newton’s laws of motion. Applications on circular motion of a particle, projectiles, rectilinear oscillatory motion of a particle, gravitational forces and satellites
  • The principle of work and kinetic energy
  • Conservation of mechanical energy theorem
  • Principle of linear impulse and momentum for a particle and application on collision of particles

Mechanics 2:

  • Planar kinematics of a rigid body: Centre of mass. Moments of inertia
  • Planar kinetics of a rigid body: Linear and angular equations
  • Applications of the equations of motion of rigid body: Translation. Rotation about a fixed axis. General plane motion
  • The principle of work and kinetic energy
  • Conservation of mechanical energy theorem
  • Principle of impulse and momentum for a rigid body
  • Introduction to vibrations