238,825 research outputs found
A general positivity-preserving algorithm for implicit high-order finite volume schemes solving the Euler and Navier-Stokes equations
This paper presents a general positivity-preserving algorithm for implicit
high-order finite volume schemes solving Euler and Navier-Stokes equations.
Previous positivity-preserving algorithms are mainly based on mathematical
analyses, being highly dependent on the existence of low-order
positivity-preserving numerical schemes for specific governing equations. This
dependency poses serious restrictions on extending these algorithms to
temporally implicit schemes, since it is difficult to know if a low-order
implicit scheme is positivity-preserving. The present positivity-preserving
algorithm is based on an asymptotic analysis of the solutions near local vacuum
minimum points. The asymptotic analysis shows that the solutions decay
exponentially with time to maintain non-negative density and pressure at a
local vacuum minimum point. In its neighborhood, the exponential evolution
leads to a modification of the linear evolution process, which can be modelled
by a direct correction of the linear residual to ensure positivity. This
correction however destroys the conservation of the numerical scheme.
Therefore, a second correction procedure is proposed to recover conservation.
The proposed positivity-preserving algorithm is considerably less restrictive
than existing algorithms. It does not rely on the existence of low-order
positivity-preserving baseline schemes and the convex decomposition of volume
integrals of flow quantities. It does not need to reduce the time step size for
maintaining the stability either. Furthermore, it can be implemented
iteratively in the implicit dual time-stepping schemes to preserve positivity
of the intermediate and converged states of the sub-iterations. It is proved
that the present positivity-preserving algorithm is accuracy-preserving.
Numerical results demonstrate that the proposed algorithm preserves the
positive density and pressure in all test cases.Comment: 52 pages, 8 figure
State of the Art in the Optimisation of Wind Turbine Performance Using CFD
Wind energy has received increasing attention in recent years due to its sustainability and geographically wide availability. The efficiency of wind energy utilisation highly depends on the performance of wind turbines, which convert the kinetic energy in wind into electrical energy. In order to optimise wind turbine performance and reduce the cost of next-generation wind turbines, it is crucial to have a view of the state of the art in the key aspects on the performance optimisation of wind turbines using Computational Fluid Dynamics (CFD), which has attracted enormous interest in the development of next-generation wind turbines in recent years. This paper presents a comprehensive review of the state-of-the-art progress on optimisation of wind turbine performance using CFD, reviewing the objective functions to judge the performance of wind turbine, CFD approaches applied in the simulation of wind turbines and optimisation algorithms for wind turbine performance. This paper has been written for both researchers new to this research area by summarising underlying theory whilst presenting a comprehensive review on the up-to-date studies, and experts in the field of study by collecting a comprehensive list of related references where the details of computational methods that have been employed lately can be obtained
Simple digital quantum algorithm for symmetric first order linear hyperbolic systems
This paper is devoted to the derivation of a digital quantum algorithm for
the Cauchy problem for symmetric first order linear hyperbolic systems, thanks
to the reservoir technique. The reservoir technique is a method designed to
avoid artificial diffusion generated by first order finite volume methods
approximating hyperbolic systems of conservation laws. For some class of
hyperbolic systems, namely those with constant matrices in several dimensions,
we show that the combination of i) the reservoir method and ii) the alternate
direction iteration operator splitting approximation, allows for the derivation
of algorithms only based on simple unitary transformations, thus perfectly
suitable for an implementation on a quantum computer. The same approach can
also be adapted to scalar one-dimensional systems with non-constant velocity by
combining with a non-uniform mesh. The asymptotic computational complexity for
the time evolution is determined and it is demonstrated that the quantum
algorithm is more efficient than the classical version. However, in the quantum
case, the solution is encoded in probability amplitudes of the quantum
register. As a consequence, as with other similar quantum algorithms, a
post-processing mechanism has to be used to obtain general properties of the
solution because a direct reading cannot be performed as efficiently as the
time evolution.Comment: 28 pages, 12 figures, major rewriting of the section describing the
numerical method, simplified the presentation and notation, reorganized the
sections, comments are welcome
Some Results on the Complexity of Numerical Integration
This is a survey (21 pages, 124 references) written for the MCQMC 2014
conference in Leuven, April 2014. We start with the seminal paper of Bakhvalov
(1959) and end with new results on the curse of dimension and on the complexity
of oscillatory integrals. Some small errors of earlier versions are corrected
Fast iteration of cocyles over rotations and Computation of hyperbolic bundles
In this paper, we develop numerical algorithms that use small requirements of
storage and operations for the computation of hyperbolic cocycles over a
rotation. We present fast algorithms for the iteration of the quasi-periodic
cocycles and the computation of the invariant bundles, which is a preliminary
step for the computation of invariant whiskered tori
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