Mehdi Vahdati

Bio: Mehdi Vahdati is an academic researcher from Imperial College London. The author has contributed to research in topics: Flutter & Aeroelasticity. The author has an hindex of 21, co-authored 101 publications receiving 2842 citations. Previous affiliations of Mehdi Vahdati include Swansea University.

Finite Element Flux-Corrected Transport (FEM-FCT) for the Euler and Navier-Stokes equations

Abstract: A high resolution finite element method for the solution of problems involving high speed compressible flows is presented. The method uses the concepts of flux-corrected transport and is presented in a form which is suitable for implementation on completely unstructured triangular or tetrahedral meshes. Transient and steady state examples are solved to illustrate the performance of the algorithm.

Modeling of Three-Dimensional Viscous Compressible Turbomachinery Flows Using Unstructured Hybrid Grids

Abstract: An advanced numerical model for the simulation of steady and unsteady viscous compressible e ows for turbomachinery applications is described. The compressible Favre-averaged Navier ‐Stokes equations are used together with a one-equation turbulence model. The e ow domain is discretized using unstructured hybrid grids that can contain a mixture of hexahedral, pentahedral, tetrahedral, and triangular prismatic cells. The e ow equations are discretized using a node-centered e nite volume scheme that relies on representing the mesh using an edge-based data structure. A dual time stepping technique is applied to a point implicit formulation so that time accuracy can be maintained with large Courant ‐Friedrichs‐Lewy numbers. Nonree ecting boundary conditions are applied at the ine ow and oute ow boundaries to prevent any spurious ree ections of the outgoing waves. The model was validated against measured data for two cases. Radial proe les of pressure and temperature rise were determined from the steady e ow analysis of a rig fan blade, and these were found to be in very good agreement with the measured quantities. A rotor/stator interaction was studied next. Detailed comparisons were carried out against measured steady and unsteady e ow data and good agreement was obtained in all cases.

FEM-FCT - Combining unstructured grids with high resolution

Abstract: The extension of flux-corrected transport (FCT) schemes to unstructured grids is presented. The spatial discretization is performed via finite elements. In particular, triangular elements in two dimensions have been chosen. The limiting procedure is based on Zalesak's (1979) extension to more than one dimension of the FCT schemes developed by Boris and Book (1973). The resulting scheme, FEM-FCT, is capable of resolving moving and stationary shocks within two elements, and several examples are given that demonstrate the accuracy attainable, even for complicated geometries.

A Posteriori Error Estimation in Finite Element Analysis

Abstract: This monograph presents a summary account of the subject of a posteriori error estimation for finite element approximations of problems in mechanics. The study primarily focuses on methods for linear elliptic boundary value problems. However, error estimation for unsymmetrical systems, nonlinear problems, including the Navier-Stokes equations, and indefinite problems, such as represented by the Stokes problem are included. The main thrust is to obtain error estimators for the error measured in the energy norm, but techniques for other norms are also discussed.

Boundary Layer Theory

Abstract: The boundary layer equations for plane, incompressible, and steady flow are $$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

A simple error estimator and adaptive procedure for practical engineerng analysis

Abstract: A new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes. The estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors. It can thus be combined with a full adaptive process of refinement or, more simply, provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials. When combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable. Estimates other than the energy norm have successfully been applied giving, for instance, a predetermined accuracy of stresses.

Computational Fluid Dynamics: Principles and Applications Ed. 3

Abstract: Computational Fluid Dynamics: Principles and Applications, Third Edition presents students, engineers, and scientists with all they need to gain a solid understanding of the numerical methods and principles underlying modern computation techniques in fluid dynamics By providing complete coverage of the essential knowledge required in order to write codes or understand commercial codes, the book gives the reader an overview of fundamentals and solution strategies in the early chapters before moving on to cover the details of different solution techniques This updated edition includes new worked programming examples, expanded coverage and recent literature regarding incompressible flows, the Discontinuous Galerkin Method, the Lattice Boltzmann Method, higher-order spatial schemes, implicit Runge-Kutta methods and parallelization An accompanying companion website contains the sources of 1-D and 2-D Euler and Navier-Stokes flow solvers (structured and unstructured) and grid generators, along with tools for Von Neumann stability analysis of 1-D model equations and examples of various parallelization techniques Will provide you with the knowledge required to develop and understand modern flow simulation codes Features new worked programming examples and expanded coverage of incompressible flows, implicit Runge-Kutta methods and code parallelization, among other topics Includes accompanying companion website that contains the sources of 1-D and 2-D flow solvers as well as grid generators and examples of parallelization techniques