Michael B. Giles

Multi-level Monte Carlo path simulation (2008)

this paper is to analyze a method for obtaining superconvergent functional estimates for arbitrary underlying numerical discretizations. The key is the use of the solution of the adjoint PDE (the...

Analytic Adjoint Solutions for the Quasi-1D Euler Equations (2007)

We show that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using Monte Carlo path simulations. In...

Report no. 01/15 Algorithm Developments for Discrete Adjoint Methods (2007)

this paper we have undertaken a detailed investigation of adjoint solutions for the quasi-1D Euler equations, focusing in particular on the solution behaviour at a shock or a sonic point where there...

Michael B. Giles, Mihai C. Duta, Niles A. Pierce

This paper presents a number of algorithm developments for adjoint methods using the `discrete ' approach in which the discretisation of the nonlinear equations is linearised and the resulting...

Report no. 95/10 Preconditioning on Stretched Meshes (2007)

Eigenmode Analysis of Boundary Conditions for the One-Dimensional Preconditioned Euler Equations (2007)

High aspect ratio cells in a computational mesh compound the inherent stiffness in the Euler and Navier--Stokes equations which arises from a disparity in the propagative speeds of convective and...

David L. Darmofal, Pierre Moinier, Michael B. Giles

The effect of local preconditioning on boundary conditions is analyzed for the subsonic, one-dimensional Euler equations. Decay rates for the eigenmodes of the initial boundary value problem are...

Adjoint Error Correction for Integral Outputs (2007)

Eigenmode Analysis for Turbomachinery Applications (2007)

These lecture notes begin by observing that in many cases the most important engineering outputs of CFD calculations are one or two integral quantities, such as the lift and drag. It is then...

Pierre Moinier, Michael B. Giles

This paper discusses the numerical computation of unsteady eigenmodes superimposed upon an annular mean ow which is uniform axially and circumferentially, but non-uniform in the radial direction....

Report no. 00/02 Improved lift and drag estimates using adjoint Euler equations (2007)

Report no. 01/18 Adjoint Error Correction for Integral Outputs (2007)

This paper demonstrates the use of adjoint error analysis to improve the order of accuracy of integral functionals obtained from CFD calculations. Using second order accurate nite element solutions...

Sharp error estimates for discretizations of the 1D convection-diffusion equation with Dirac initial data (2007)

These lecture notes begin by observing that in many cases the most important engineering outputs of CFD calculations are one or two integral quantities, such as the lift and drag. It is then...

Carter, Rebecca, Giles, Michael B.

This paper derives sharp estimates of the error arising from explicit and implicit approximations of the constant-coefficient 1D convection–diffusion equation with Dirac initial data. The error...

Sharp error estimates for discretizations of the 1D convection-diffusion equation with Dirac initial data (2007)

Carter, Rebecca, Giles, Michael B.

This paper derives sharp estimates of the error arising from explicit and implicit approximations of the constant-coefficient 1D convection–diffusion equation with Dirac initial data. The error...

Sharp error estimates for a discretisation of the 1D convection/diffusion equation with Dirac initial data (2004)

Fluid Dynamics of High Performance Turbomachines. (2002)

This paper derives sharp l and l 1 estimates of the error arising from an explicit approximation of the constant coe#cient 1D convection/di#usion equation with Dirac initial data. The analysis embeds...

Greitzer,Edward M., Epstein,Alan H., Giles,Michael B., McCunme,James E., Tan,Choon S.

This report describes work which is part of a study on high performance turbomachinery fluid dynamics. Within the general topic, four separate tasks studies include: 1) Loss mechanisms and loss...

Fluid Dynamics of High Performance Turbomachines. (2002)

Greitzer,Edward M., Epstein,Alan H., Giles,Michael B., Kerrebrock,Jack L., McCune,James E.

Major tasks include: 1) Loss mechanisms and loss migration in transonic compressors, including development of advanced instrumentation for measurements of wake radial transport and analysis of...

Discrete adjoint approximations with shocks (2002)

Stabilization of a Linearized Navier-Stokes Solver for Turbomachinery Aeroelasticity (2002)

This paper is concerned with the formulation and discretisation of adjoint equations when there are shocks in the underlying solution to the original nonlinear hyperbolic p.d.e. For the model problem...

M. Sergio Campobasso, Michael B. Giles

The linear analysis of turbomachinery aeroelasticity relies on the assumption of small level of unsteadiness and requires the solution of both the nonlinear steady and the linear unsteady ow...

Analytic adjoint solutions for the quasi-one-dimensional Euler equations (2001)

Giles, Michael B., Pierce, Niles A.

The analytic properties of adjoint solutions are examined for the quasi-one-dimensional Euler equations. For shocked flow, the derivation of the adjoint problem reveals that the adjoint variables are...

Analytic Adjoint Solutions for the Quasi-1D Euler Equations (2001)

Michael B Giles, Niles A Pierce

this paper we have undertaken a detailed investigation of adjoint solutions for the quasi-1D Euler equations, focusing in particular on the solution behaviour at a shock or a sonic point where there...

Adjoint Code Developments Using the Exact Discrete Approach (2001)

Michael B. Giles, Michael B. Giles, Jens-Dominik Müller, Mihai C. Duta, Mihai C. Duta

This paper presents a number of algorithm developments for adjoint methods using the `discrete' approach in which the discretisation of the nonlinear equations is linearised and the resulting...

Adjoint recovery of superconvergent functionals from PDE approximations (2000)

Pierce, Niles A., Giles, Michael B.

Motivated by applications in computational fluid dynamics, a method is presented for obtaining estimates of integral functionals, such as lift or drag, that have twice the order of accuracy of the...

An introduction to the adjoint approach to design (2000)

Defect and Adjoint Error Correction (2000)

Abstract. Optimal design methods involving the solution of an adjoint system of equations are an active area of research in computational uid dynamics, particularly for aeronautical applications....

Eigenmode Analysis of Boundary Conditions for the One-dimensional Preconditioned Euler Equations (2000)

Motivated by applications in aero-acoustics and electromagnetics, this paper discusses the combined use of defect correction to improve the order of accuracy of numerical solutions, and adjoint error...

David L. Darmofal, Pierre Moinier, Michael B. Giles

this paper is to analyze the eect of preconditioning on several different boundary conditions commonly used in numerical simulations. Specically, we consider the one-dimensional, preconditioned Euler...

An Introduction to the Adjoint Approach to Design (2000)

On the Iterative Solution of Adjoint Equations (2000)

This paper presents an introduction to the subject, emphasising the simplicity of the ideas when viewed in the context of linear algebra. Detailed discussions also include the extension to...

Improved lift and drag estimates using adjoint Euler equations (1999)

This paper considers the iterative solution of the adjoint equations which arise in the context of design optimisation. It is shown that naive adjoining of the iterative solution of the original...

Edge-based multigrid and preconditioning for hybrid grids (1999)

This paper demonstrates the use of adjoint error analysis to improve the order of accuracy of integral functionals obtained from CFD calculations. Using second order accurate finite element solutions...

Pierre Moinier, Pierre Moinier, Jens-dominik Muller, Michael B. Giles, Michael B. Giles

A multigrid method has been developed for the Euler and Navier-Stokes equations on unstructured hybrid grids in two and three dimensions. The coarse grids are automatically generated from the finest...

Air Force Research in Aero Propulsion Technology. (1998)

Greitzer, Edward M., Epstein, Alan H., Tan, Choon S., Giles, Michael B., Martinez-Sanchez, Manuel

The work consisted of six separate projects: 1. Rotor Dynamic Instability due to Alford Forces; 2. Turbocharger Stall; 3. Three-Dimensional Flows in Turbomachines; 4. Computational Techniques for...

Fluid Dynamics of High Performance Turbomachines. (1998)

Greitzer, Edward M., Epstein, Alan H., Giles, Michael B., McCune, James E., Tan, Choon S.

Within the general topic, four separate tasks are specified. These are, in brief: I. Loss mechanisms and loss migration in transonic compressors, including development of advanced instrumentation for...

Unsteady Flow Phenomena in Turbomachines. (1998)

Greitzer, Edward M., Epstein, Alan H., Giles, Michael B., McCune, James E., Tan, Choon S.

This report describes work carried out at the Gas Turbine Laboratory at M.I.T. as part of our multi-investigator effort on basic unsteady flow phenomena. Within the overall project, four separate...

On the properties of solutions of the adjoint Euler equations (1998)

Edge-based multigrid schemes for hybrid grids (1998)

The behavior of analytic and numerical adjoint solutions is examined for the quasi-1D Euler equations. For shocked flow, the derivation of the adjoint problem reveals that the adjoint variables are...

Jens-dominik Muller, Michael B. Giles

A Navier-Stokes multigrid method that has been developed for triangles and tetrahedra is extended to be used on hybrid grids. Various choices in extending the linear preserving flux calculation of...

Adjoint Recovery of Superconvergent Functionals from PDE Approximations (1998)

Adjoint Recovery of Superconvergent Functionals from Approximate Solutions of Partial Differential Equations (1998)

. Motivated by applications in computational uid dynamics, this paper presents a method for obtaining estimates of integral functionals, such as lift or drag, that have twice the order of accuracy of...

Preconditioned Multigrid Methods for Compressible Flow Calculations on Stretched Meshes (1997)

this paper can therefore be viewed as extending superconvergence theory to cover numerical results obtained by any numerical method: finite difference, finite volume or finite element without natural...

Preconditioning compressible flow calculations on stretched meshes (1996)

this paper are not intended for preconditioning in the limit of incompressibility. For typical viscous meshes, the Mach number remains sufficiently large, even in the cells near the wall, that the...