440 research outputs found
A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow
We present an efficient discontinuous Galerkin scheme for simulation of the
incompressible Navier-Stokes equations including laminar and turbulent flow. We
consider a semi-explicit high-order velocity-correction method for time
integration as well as nodal equal-order discretizations for velocity and
pressure. The non-linear convective term is treated explicitly while a linear
system is solved for the pressure Poisson equation and the viscous term. The
key feature of our solver is a consistent penalty term reducing the local
divergence error in order to overcome recently reported instabilities in
spatially under-resolved high-Reynolds-number flows as well as small time
steps. This penalty method is similar to the grad-div stabilization widely used
in continuous finite elements. We further review and compare our method to
several other techniques recently proposed in literature to stabilize the
method for such flow configurations. The solver is specifically designed for
large-scale computations through matrix-free linear solvers including efficient
preconditioning strategies and tensor-product elements, which have allowed us
to scale this code up to 34.4 billion degrees of freedom and 147,456 CPU cores.
We validate our code and demonstrate optimal convergence rates with laminar
flows present in a vortex problem and flow past a cylinder and show
applicability of our solver to direct numerical simulation as well as implicit
large-eddy simulation of turbulent channel flow at as well as
.Comment: 28 pages, in preparation for submission to Journal of Computational
Physic
Numerical solving unsteady space-fractional problems with the square root of an elliptic operator
An unsteady problem is considered for a space-fractional equation in a
bounded domain. A first-order evolutionary equation involves the square root of
an elliptic operator of second order. Finite element approximation in space is
employed. To construct approximation in time, regularized two-level schemes are
used. The numerical implementation is based on solving the equation with the
square root of the elliptic operator using an auxiliary Cauchy problem for a
pseudo-parabolic equation. The scheme of the second-order accuracy in time is
based on a regularization of the three-level explicit Adams scheme. More
general problems for the equation with convective terms are considered, too.
The results of numerical experiments are presented for a model two-dimensional
problem.Comment: 21 pages, 7 figures. arXiv admin note: substantial text overlap with
arXiv:1412.570
Robust and efficient discontinuous Galerkin methods for under-resolved turbulent incompressible flows
We present a robust and accurate discretization approach for incompressible
turbulent flows based on high-order discontinuous Galerkin methods. The DG
discretization of the incompressible Navier-Stokes equations uses the local
Lax-Friedrichs flux for the convective term, the symmetric interior penalty
method for the viscous term, and central fluxes for the velocity-pressure
coupling terms. Stability of the discretization approach for under-resolved,
turbulent flow problems is realized by a purely numerical stabilization
approach. Consistent penalty terms that enforce the incompressibility
constraint as well as inter-element continuity of the velocity field in a weak
sense render the numerical method a robust discretization scheme in the
under-resolved regime. The penalty parameters are derived by means of
dimensional analysis using penalty factors of order 1. Applying these penalty
terms in a postprocessing step leads to an efficient solution algorithm for
turbulent flows. The proposed approach is applicable independently of the
solution strategy used to solve the incompressible Navier-Stokes equations,
i.e., it can be used for both projection-type solution methods as well as
monolithic solution approaches. Since our approach is based on consistent
penalty terms, it is by definition generic and provides optimal rates of
convergence when applied to laminar flow problems. Robustness and accuracy are
verified for the Orr-Sommerfeld stability problem, the Taylor-Green vortex
problem, and turbulent channel flow. Moreover, the accuracy of high-order
discretizations as compared to low-order discretizations is investigated for
these flow problems. A comparison to state-of-the-art computational approaches
for large-eddy simulation indicates that the proposed methods are highly
attractive components for turbulent flow solvers
Solutions to Three-Dimensional Thin-Layer Navier-Stokes Equations in Rotating Coordinates for Flow Through Turbomachinery
The viscous, Navier-Stokes solver for turbomachinery applications, MSUTC has been modified to include the rotating frame formulation. The three-dimensional thin-layer Navier-Stokes equations have been cast in a rotating Cartesian frame enabling the freezing of grid motion. This also allows the flow-field associated with an isolated rotor to be viewed as a steady-state problem. Consequently, local time stepping can be used to accelerate convergence. The formulation is validated by running NASA's Rotor 67 as the test case. results are compared between the rotating frame code and the absolute frame code. The use of the rotating frame approach greatly enhances the performance of the code with respect to savings in computing time, without degradation of the solution
A high-order artificial compressibility method based on Taylor series time-stepping for variable density flow
In this paper, we introduce a fourth-order accurate finite element method for
incompressible variable density flow. The method is implicit in time and
constructed with the Taylor series technique, and uses standard high-order
Lagrange basis functions in space. Taylor series time-stepping relies on time
derivative correction terms to achieve high-order accuracy. We provide detailed
algorithms to approximate the time derivatives of the variable density
Navier-Stokes equations. Numerical validations confirm a fourth-order accuracy
for smooth problems. We also numerically illustrate that the Taylor series
method is unsuitable for problems where regularity is lost by solving the 2D
Rayleigh-Taylor instability problem
Isogeometric finite element methods for liquid metal magnetohydrodynamics
A fusion blanket is a key component in a fusion reactor which extracts heat energy, protects the surrounding structure and possibly produces tritium, one of the fuels required for the deuterium-tritium fusion reaction. Interest in magneto-hydrodynamic (MHD) effects in the fusion blanket has been growing due to the promising prospect of a liquid breeder blanket, due to its high power density and the possibility of sustainable production of tritium. However, MHD effects can significantly influence the operating performance of the fusion blanket and an accurate and reliable analysis of the MHD effects are critical in its design. Significant progress in the numerical study of MHD has been made recently, due in large part to the advancement in computing power. However, its maturity has not yet reached a point comparable with standard CFD solvers. In particular, complex domains and complex externally applied magnetic fields present additional challenges for numerical schemes in MHD. For that reason, the application of isogeometric analysis is considered in this thesis. Isogeometric Analysis (IGA) is a new class of numerical method which integrates Computer Aided Design (CAD) into Finite Element Analysis (FEA). In IGA, B-splines and NURBS, which are the building blocks used to construct a geometry in CAD, are also used to build the finite element spaces. This allows to represent geometries more accurately, and in some cases exactly. This may help advance the progress of numerical studies of MHD effects, not only in fusion blanket scenarios, but more widely. In this thesis, we develop and study a number of types of IGA based MHD solver; a fully-developed MHD flow solver, a steady-state MHD solver and a time-dependent MHD solver. These solvers are validated using analytical methods and methods of manufactured solution and are compared with other numerical schemes on a number of benchmark problems.Open Acces
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