184 research outputs found
A relaxation method for large eigenvalue problems, with an application to flow stability analysis
International audienceLinear stability analysis of fluid flows usually involves the numerical solution of large eigenvalue problems. We present a spectral transformation allowing the computation of the least stable eigenmodes in a prescribed frequency range, based on the filtering of the linearized equations of motion. This "shift-relax" method has the advantage of low memory requirements and is therefore suitable for large two- or three-dimensional problems. For demonstration purposes, this new method is applied to compute eigenmodes of a compressible jet
ICASE semiannual report, April 1 - September 30, 1989
The Institute conducts unclassified basic research in applied mathematics, numerical analysis, and computer science in order to extend and improve problem-solving capabilities in science and engineering, particularly in aeronautics and space. The major categories of the current Institute for Computer Applications in Science and Engineering (ICASE) research program are: (1) numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; (2) control and parameter identification problems, with emphasis on effective numerical methods; (3) computational problems in engineering and the physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and (4) computer systems and software, especially vector and parallel computers. ICASE reports are considered to be primarily preprints of manuscripts that have been submitted to appropriate research journals or that are to appear in conference proceedings
Implicit time integration for high-order compressible flow solvers
The application of high-order spectral/hp element discontinuous Galerkin (DG)
methods to unsteady compressible flow simulations has gained increasing popularity.
However, the time step is seriously restricted when high-order methods are applied
to an explicit solver. To eliminate this restriction, an implicit high-order compressible flow solver is developed using DG methods for spatial discretization, diagonally
implicit Runge-Kutta methods for temporal discretization, and the Jacobian-free
Newton-Krylov method as its nonlinear solver. To accelerate convergence, a block
relaxed Jacobi preconditioner is partially matrix-free implementation with a hybrid
calculation of analytical and numerical Jacobian.The problem of too many user-defined parameters within the implicit solver is
then studied. A systematic framework of adaptive strategies is designed to relax the
difficulty of parameter choices. The adaptive time-stepping strategy is based on the
observation that in a fixed mesh simulation, when the total error is dominated by the
spatial error, further decreasing of temporal error through decreasing the time step
cannot help increase accuracy but only slow down the solver. Based on a similar
error analysis, an adaptive Newton tolerance is proposed based on the idea that
the iterative error should be smaller than the temporal error to guarantee temporal
accuracy. An adaptive strategy to update the preconditioner based on the Krylov
solver’s convergence state is also discussed. Finally, an adaptive implicit solver is
developed that eliminates the need for repeated tests of tunning parameters, whose
accuracy and efficiency are verified in various steady/unsteady simulations. An improved shock-capturing strategy is also proposed when the implicit solver
is applied to high-speed simulations. Through comparisons among the forms of
three popular artificial viscosities, we identify the importance of the density term
and add density-related terms on the original bulk-stress based artificial viscosity.
To stabilize the simulations involving strong shear layers, we design an extra shearstress based artificial viscosity. The new shock-capturing strategy helps dissipate
oscillations at shocks but has negligible dissipation in smooth regions.Open Acces
Physics based GMRES preconditioner for compressible and incompressible Navier-Stokes equations
This paper presents the implementation of a local physics preconditioning mass matrix [8] for an unified approach of 3D compressible and incompressible Navier-Stokes equations using an SUPG finite element formulation and GMRES implicit solver. During the last years a lot of effort has been dedicated to finding a unified approach for compressible and incompressible flow in order to treat fluid dynamic problems with a very wide range of Mach and Reynolds numbers [10,26,37]. On the other hand, SUPG finite element formulation and GMRES implicit solver is one of the most robust combinations to solve state of the art CFD problems [1,6,9,22,29,30,31].
The selection of a good preconditioner and its performance on parallel architecture is another open problem in CFD community. The local feature of the preconditioner presented here means that no communication among processors is needed when working on parallel architectures. Due to these facts we consider that this research can make some contributions towards the development of a unified fluid dynamic model with high rates of convergence for any combination of Mach and Reynolds numbers, being very suitable for massively parallel computations.
Finally, it is important to remark that while this kind of preconditioning produces stabilized results in nearly incompressible regimes the standard version exhibits some numerical drawbacks that lead to solutions without physical meaning
Four Decades of Studying Global Linear Instability: Progress and Challenges
Global linear instability theory is concerned with the temporal or spatial development of small-amplitude
perturbations superposed upon laminar steady or time-periodic three-dimensional flows, which are inhomogeneous in two(and periodic in one)or all three spatial directions.After a brief exposition of the theory,some recent advances are reported. First, results are presented on the implementation of a Jacobian-free Newton–Krylov time-stepping method into a standard
finite-volume aerodynamic code to obtain global linear instability results in flows of industrial interest. Second, connections are sought between established and more-modern approaches for structure identification in
flows, such as proper orthogonal decomposition and Koopman modes analysis (dynamic mode decomposition), and the possibility to connect solutions of the eigenvalue problem obtained by matrix formation or time-stepping with those delivered by dynamic mode decomposition, residual algorithm, and proper orthogonal decomposition analysis is highlighted in the laminar regime; turbulent and three-dimensional flows are identified as open areas for future research. Finally, a new stable very-high-order finite-difference method is implemented for the
spatial discretization of the operators describing the spatial biglobal eigenvalue problem, parabolized stability
equation three-dimensional analysis, and the triglobal eigenvalue problem; it is shown that, combined with sparse
matrix treatment, all these problems may now be solved on standard desktop computer
Global linear stability of a model subsonic jet
The global stability of a subsonic jet is investigated using a model base flow designed to fit experimental results for turbulent mean flows. Eigenmodes are computed for axisymmetric perturbations in order to investigate the nature of typically observed large-scale coherent oscillations ("preferred mode"). We do not find evidence that this preferred mode corre- sponds to the least damped global mode. Non-modal stability is also considered through the computation of optimal perturbations. Although non-axisymmetric perturbations (in particular for azimuthal wavenumber m = 1) are subject to larger transient growth, these reach their peak amplitude far downstream of the potential core, and therefore they are less likely to be observed
Modal and transient dynamics of jet flows
International audienceThe linear stability dynamics of incompressible and compressible isothermal jets are investigated by means of their optimal initial perturbations and of their temporal eigenmodes. The transient growth analysis of optimal perturbations is robust and allows physical interpretation of the salient instability mechanisms. In contrast, the modal representation appears to be inadequate, as neither the computed eigenvalue spectrum nor the eigenmode shapes allow a characterization of the flow dynamics in these settings. More surprisingly, numerical issues also prevent the reconstruction of the dynamics from a basis of computed eigenmodes. An investigation of simple model problems reveals inherent problems of this modal approach in the context of a stable convection-dominated configuration. In particular, eigenmodes may exhibit an exponential growth in the streamwise direction even in regions where the flow is locally stable
An effective preconditioning strategy for volume penalized incompressible/low Mach multiphase flow solvers
The volume penalization (VP) or the Brinkman penalization (BP) method is a
diffuse interface method for simulating multiphase fluid-structure interaction
(FSI) problems in ocean engineering and/or phase change problems in thermal
sciences. The method relies on a penalty factor (which is inversely related to
body's permeability ) that must be large to enforce rigid body velocity
in the solid domain. When the penalty factor is large, the discrete system of
equations becomes stiff and difficult to solve numerically. In this paper, we
propose a projection method-based preconditioning strategy for solving volume
penalized (VP) incompressible and low-Mach Navier-Stokes equations. The
projection preconditioner enables the monolithic solution of the coupled
velocity-pressure system in both single phase and multiphase flow settings. In
this approach, the penalty force is treated implicitly, which is allowed to
take arbitrary large values without affecting the solver's convergence rate or
causing numerical stiffness/instability. It is made possible by including the
penalty term in the pressure Poisson equation. Solver scalability under grid
refinement is demonstrated. A manufactured solution in a single phase setting
is used to determine the spatial accuracy of the penalized solution.
Second-order pointwise accuracy is achieved for both velocity and pressure
solutions. Two multiphase fluid-structure interaction (FSI) problems from the
ocean engineering literature are also simulated to evaluate the solver's
robustness and performance. The proposed solver allows us to investigate the
effect of on the motion of the contact line over the surface of the
immersed body. It also allows us to investigate the dynamics of the free
surface of a solidifying meta
A Jacobian-free Newton-Krylov method for time-implicit multidimensional hydrodynamics
This work is a continuation of our efforts to develop an efficient implicit
solver for multidimensional hydrodynamics for the purpose of studying important
physical processes in stellar interiors, such as turbulent convection and
overshooting. We present an implicit solver that results from the combination
of a Jacobian-Free Newton-Krylov method and a preconditioning technique
tailored to the inviscid, compressible equations of stellar hydrodynamics. We
assess the accuracy and performance of the solver for both 2D and 3D problems
for Mach numbers down to . Although our applications concern flows in
stellar interiors, the method can be applied to general advection and/or
diffusion-dominated flows. The method presented in this paper opens up new
avenues in 3D modeling of realistic stellar interiors allowing the study of
important problems in stellar structure and evolution.Comment: Accepted for publication in A&
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