277 research outputs found
A novel convergence enhancement method based on Online Dimension Reduction Optimization
Iterative steady-state solvers are widely used in computational fluid
dynamics. Unfortunately, it is difficult to obtain steady-state solution for
unstable problem caused by physical instability and numerical instability.
Optimization is a better choice for solving unstable problem because
steady-state solution is always the extreme point of optimization regardless of
whether the problem is unstable or ill-conditioned, but it is difficult to
solve partial differential equations (PDEs) due to too many optimization
variables. In this study, we propose an Online Dimension Reduction Optimization
(ODRO) method to enhance the convergence of the traditional iterative method to
obtain the steady-state solution of unstable problem. This method performs
proper orthogonal decomposition (POD) on the snapshots collected from a few
iteration steps, optimizes PDE residual in the POD subspace to get a solution
with lower residual, and then continues to iterate with the optimized solution
as the initial value, repeating the above three steps until the residual
converges. Several typical cases show that the proposed method can efficiently
calculate the steady-state solution of unstable problem with both the high
efficiency and robustness of the iterative method and the good convergence of
the optimization method. In addition, this method is easy to implement in
almost any iterative solver with minimal code modification
Spectral/hp element methods: recent developments, applications, and perspectives
The spectral/hp element method combines the geometric flexibility of the
classical h-type finite element technique with the desirable numerical
properties of spectral methods, employing high-degree piecewise polynomial
basis functions on coarse finite element-type meshes. The spatial approximation
is based upon orthogonal polynomials, such as Legendre or Chebychev
polynomials, modified to accommodate C0-continuous expansions. Computationally
and theoretically, by increasing the polynomial order p, high-precision
solutions and fast convergence can be obtained and, in particular, under
certain regularity assumptions an exponential reduction in approximation error
between numerical and exact solutions can be achieved. This method has now been
applied in many simulation studies of both fundamental and practical
engineering flows. This paper briefly describes the formulation of the
spectral/hp element method and provides an overview of its application to
computational fluid dynamics. In particular, it focuses on the use the
spectral/hp element method in transitional flows and ocean engineering.
Finally, some of the major challenges to be overcome in order to use the
spectral/hp element method in more complex science and engineering applications
are discussed
CAD-based CFD shape optimisation using discrete adjoint solvers
Computational
fluid dynamics is reaching a level of maturity that it can be
used as a predictive tool. Consequently, simulation-driven product design and
optimisation is starting to be deployed for industrial applications. When performing
gradient-based aerodynamic shape optimisation for industrial applications,
adjoint method is preferable as it can compute the design gradient of
a small number of objective functions with respect to a large number of design
variables efficiently. However, for certain industrial cases, the iterative calculation
of steady state nonlinear flow solver based on the Reynolds-averaged
Navier{Stokes equations tends to fail to converge asymptotically. For such
cases, the adjoint solver usually diverges exponentially, due to the inherited
linear instability from the non-converged nonlinear flow. A method for stabilising
both the nonlinear flow and the adjoint solutions via an improved timestepping
method is developed and applied successfully to industrial relevant
test cases. Another challenge in shape optimisation is the shape parametrisation
method. A good parametrisation should represent a rich design space to
be explored and at the same time be flexible to take into account the various
geometric constraints. In addition, it is preferable to be able to transform
from the parametrisation to a format readable by most CAD software, such
as the STEP le. A novel NURBS-based parametrisation method is developed
that uses the control points of the NURBS patches as design variables.
In addition, a test-point approach is used to impose various geometric constraints.
The parametrisation is fully compatible with most CAD software.
The NURBS-based parametrisation is applied to several industrial cases
Solving an inverse coupled conjugate heat transfer problem by an adjoint approach
A framework for obtaining adjoint gradients for coupled conjugate heat
transfer problems is presented. The framework is tailored to partitioned approaches in
which separate solvers are used for the fluid and solid domains. The exchange of sensitiv- ities
between adjoint fluid and solid solvers is necessary in order to obtain gradients and how this is
achieved is described. The effectiveness of the procedure is demonstrated by solving a conjugate
heat transfer problem using a gradient based approach. The presented method can be extended to
sensitivity analysis of multidisciplinary problems where both
solvers offer adjoint derivatives
Robust and stable discrete adjoint solver development for shape optimisation of incompressible flows with industrial applications
PhD, 156ppThis thesis investigates stabilisation of the SIMPLE-family discretisations for incompressible
flow and their discrete adjoint counterparts. The SIMPLE method is
presented from typical \prediction-correction" point of view, but also using a pressure
Schur complement approach, which leads to a wider class of schemes. A novel semicoupled
implicit solver with velocity coupling is proposed to improve stability. Skewness
correction methods are applied to enhance solver accuracy on non-orthogonal
grids. An algebraic multi grid linear solver from the HYPRE library is linked to
flow and discrete adjoint solvers to further stabilise the computation and improve
the convergence rate. With the improved implementation, both of
flow and discrete adjoint solvers can be applied to a wide range of 2D and 3D test cases. Results
show that the semi-coupled implicit solver is more robust compared to the standard
SIMPLE solver. A shape optimisation of a S-bend air flow duct from a VW Golf
vehicle is studied using a CAD-based parametrisation for two Reynolds numbers.
The optimised shapes and their flows are analysed to con rm the physical nature of
the improvement.
A first application of the new stabilised discrete adjoint method to a reverse osmosis
(RO) membrane channel flow is presented. A CFD model of the RO membrane
process with a membrane boundary condition is added. Two objective functions,
pressure drop and permeate flux, are evaluated for various spacer geometries such as
open channel, cavity, submerged and zigzag spacer arrangements. The flow and the
surface sensitivity of these two objective functions is computed and analysed for these
geometries. An optimisation with a node-base parametrisation approach is carried
out for the zigzag con guration channel flow in order to reduce the pressure drop.
Results indicate that the pressure loss can be reduced by 24% with a slight reduction
in permeate flux by 0.43%.Queen Mary-China Scholarship Council Co-funded Scholarship No. 201206280018
Iterative Methods for Problems in Computational Fluid Dynamics
We discuss iterative methods for solving the algebraic systems of equations arising from linearization and discretization of primitive variable formulations of the incompressible Navier-Stokes equations. Implicit discretization in time leads to a coupled but linear system of partial differential equations at each time step, and discretization in space then produces a series of linear algebraic systems. We give an overview of commonly used time and space discretization techniques, and we discuss a variety of algorithmic strategies for solving the resulting systems of equations. The emphasis is on preconditioning techniques, which can be combined with Krylov subspace iterative methods. In many cases the solution of subsidiary problems such as the discrete convection-diffusion equation and the discrete Stokes equations plays a crucial role. We examine iterative techniques for these problems and show how they can be integrated into effective solution algorithms for the Navier-Stokes equations
A Mixed Hybrid Finite Volumes Solver for Robust Primal and Adjoint CFD
PhDIn the context of gradient-based numerical optimisation, the adjoint method is an e cient
way of computing the gradient of the cost function at a computational cost independent
of the number of design parameters, which makes it a captivating option for industrial
CFD applications involving costly primal solves. The method is however a ected by
instabilities, some of which are inherited from the primal solver, notably if the latter does
not fully converge. The present work is an attempt at curbing primal solver limitations
with the goal of indirectly alleviating adjoint robustness issues.
To that end, a novel discretisation scheme for the steady-state incompressible Navier-
Stokes problem is proposed: Mixed Hybrid Finite Volumes (MHFV). The scheme draws
inspiration from the family of Mimetic Finite Di erences and Mixed Virtual Elements
strategies, rid of some limitations and numerical artefacts typical of classical Finite Volumes
which may hinder convergence properties. Derivation of MHFV operators is illustrated
and each scheme is validated via manufactured solutions: rst for pure anisotropic
di usion problems, then convection-di usion-reaction and nally Navier-Stokes. Traditional
and novel Navier-Stokes solution algorithms are also investigated, adapted to
MHFV and compared in terms of performance.
The attention is then turned to the discrete adjoint Navier-Stokes system, which is assembled
in an automated way following the principles of Equational Di erentiation, i.e. the
di erentiation of the primal discrete equations themselves rather than the algorithm
used to solve them. Practical/computational aspects of the assembly are discussed, then
the adjoint gradient is validated and a few solution algorithms for the MHFV adjoint
Navier-Stokes are proposed and tested. Finally, two examples of full shape optimisation
procedures on internal ow test cases (S-bend and U-bend) are reported.European Union's Seventh Framework Programme
grant agreement number 317006
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