In this paper, we present a numerical study of the wall jet flow over a convex surface, viz. the Coanda wall jet, and its application to a conceptual Unmanned Aerial Vehicle (UAV) design which uses the Coanda effect a...
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ISBN:
(纸本)9783319257273;9783319257259
In this paper, we present a numerical study of the wall jet flow over a convex surface, viz. the Coanda wall jet, and its application to a conceptual Unmanned Aerial Vehicle (UAV) design which uses the Coanda effect as a basis of lift production. This configuration is important in a way that it considers the Coanda wall jet over a smooth convex wall with non-constant curvature, in contrast to most of the previous situations where only constant curvature walls were considered e.g. the Coanda wall jet over circular cylinder. To enable the mathematical representation of this complex geometrical configuration, we propose a form of a parametric representation of the conceptual geometry, based on Bernstein polynomials, which is universal in character and spans a complete design space. It is shown how dynamically changing the flow picture enables smooth change of net forces on the body. Capability to control the direction of the net force is shown to be useful for maneuvering the UAV. All simulations are done using an open-source finite-volume computational fluid dynamics code based on Reynolds-averaged Navier-Stokes equations. Turbulence is accounted for using the k-omega Shear Stress Transport model.
We sketch a modal tau approach for treating binary neutron stars, in particular a low-rank technique for dealing with the changing surface of a tidally distorted star.
ISBN:
(纸本)9783319198002;9783319197999
We sketch a modal tau approach for treating binary neutron stars, in particular a low-rank technique for dealing with the changing surface of a tidally distorted star.
This paper is devoted to the numerical solution of the scalar convection- diffusion- reaction equation. We present new results of the adaptive technique for computing the stabilization parameter t in the streamline up...
ISBN:
(纸本)9783319257273;9783319257259
This paper is devoted to the numerical solution of the scalar convection- diffusion- reaction equation. We present new results of the adaptive technique for computing the stabilization parameter t in the streamline upwind/Petrov-Galerkin (SUPG) method based on minimizing the value of a functional called error indicator. Particularly, we present results for conforming finite element spaces up to the order 5 with the parameter t from the piecewise discontinuous finite element spaces, also up to the order 5.
We review our recent work on multiresolution shape optimisation and present its application to elastic solids, electrostatic field equations and thin-shells. In the spirit of isogeometric analysis the geometry of the ...
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ISBN:
(数字)9783319233154
ISBN:
(纸本)9783319233154;9783319233147
We review our recent work on multiresolution shape optimisation and present its application to elastic solids, electrostatic field equations and thin-shells. In the spirit of isogeometric analysis the geometry of the domain is described with subdivision surfaces and different resolutions of the same surface are used for optimisation and analysis. The analysis is performed using a sufficiently fine control mesh with a fixed resolution. During shape optimisation the geometry is updated starting with the coarsest control mesh and then moving on to increasingly finer control meshes. The transfer of data between the geometry and analysis representations is accomplished with subdivision refinement and coarsening operators. Moreover, we discretise elastic solids with the immersed finite element method, electrostatic field equations with the boundary element method and thin-shells with the subdivision finite element technique. In all three discretisation techniques there is no need to generate and maintain an analysis-suitable volume discretisation.
There has been much work in the area of superconvergent error analysis for finite element and discontinuous Galerkin (DG) methods. The property of superconvergence leads to the question of how to exploit this informat...
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ISBN:
(纸本)9783319198002;9783319197999
There has been much work in the area of superconvergent error analysis for finite element and discontinuous Galerkin (DG) methods. The property of superconvergence leads to the question of how to exploit this information in a useful manner, mainly through superconvergence extraction. There are many methods used for superconvergence extraction such as projection, interpolation, patch recovery and B-spline convolution filters. This last method falls under the class of Smoothness-Increasing Accuracy-Conserving (SIAC) filters. It has the advantage of improving both smoothness and accuracy of the approximation. Specifically, for linear hyperbolic equations it can improve the order of accuracy of a DG approximation from k + 1 to 2k + 1, where k is the highest degree polynomial used in the approximation, and can increase the smoothness to k - 1. In this article, we discuss the importance of overcoming the mathematical barriers in making superconvergence extraction techniques useful for applications, specifically focusing on SIAC filtering.
The performance of a hybrid compact (Compact) finite difference scheme and characteristic-wise weighted essentially non-oscillatory (WENO) finite difference scheme (Hybrid) for the detonation waves simulations is inve...
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ISBN:
(纸本)9783319198002;9783319197999
The performance of a hybrid compact (Compact) finite difference scheme and characteristic-wise weighted essentially non-oscillatory (WENO) finite difference scheme (Hybrid) for the detonation waves simulations is investigated. The Hybrid scheme employs the nonlinear 5th-order WENO-Z scheme to capture high gradients and discontinuities in an essentially nonoscillatory manner and the linear 6th-order Compact scheme to resolve the fine scale structures in the smooth regions of the solution in an efficient and accurate manner. Numerical oscillations generated by the Compact scheme is mitigated by the high order filtering. The high order multi-resolution algorithm is employed to detect the smoothness of the solution. The Hybrid scheme allows a potential speedup up to a factor of three or more for certain classes of shocked problems. The simulations of one-dimensional shock-entropy wave interaction and classical stable detonation waves, and the two-dimensional detonation diffraction problem around a 90 degrees corner show that the Hybrid scheme is more efficient, less dispersive and less dissipative than the WENO-Z scheme.
This article centers on the computational performance of the continuous and discontinuous Galerkin time stepping schemes for general first-order initial value problems in R-n, with continuous nonlinearities. We briefl...
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ISBN:
(纸本)9783319198002;9783319197999
This article centers on the computational performance of the continuous and discontinuous Galerkin time stepping schemes for general first-order initial value problems in R-n, with continuous nonlinearities. We briefly review a recent existence result for discrete solutions from Janssen and Wihler (Existence results for the continuous and discontinuous Galerkin time stepping methods for nonlinear initial value problems, 2014, Submitted), and provide a numerical comparison of the two time discretization methods.
This note describes an implementation of a discontinuous Petrov Galerkin (DPG) method for acoustic waves within the framework of high order finite elements provided by the software package NGSolve. A technique to impo...
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ISBN:
(纸本)9783319198002;9783319197999
This note describes an implementation of a discontinuous Petrov Galerkin (DPG) method for acoustic waves within the framework of high order finite elements provided by the software package NGSolve. A technique to impose the impedance boundary condition weakly is indicated. Numerical results from this implementation show that a multiplicative Schwarz algorithm, with no coarse solve, provides a p-preconditioner for solving the DPG system. The numerical observations suggest that the condition number of the preconditioned system is independent of the frequency k and the polynomial degree p.
In this paper we present an assessment of the discontinuous Galerkin (DG) formulation through modified equation analysis (MEA). When applied to linear advection, MEA can help to clarify wave-propagation properties pre...
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ISBN:
(纸本)9783319198002;9783319197999
In this paper we present an assessment of the discontinuous Galerkin (DG) formulation through modified equation analysis (MEA). When applied to linear advection, MEA can help to clarify wave-propagation properties previously observed in DG. In particular, a connection between MEA and dispersion-diffusion (eigensolution) analysis is highlighted. To the authors' knowledge this is the first application of MEA to DG schemes, and as such this study focuses only on element-wise constant and linear discretizations in one dimension. For the linear discretization, we found that the physical mode's accuracy can be increased via upwinding. MEA's application to higher order solutions and non-linear problems is also briefly discussed. In special, we point out that MEA's applicability in the analysis of DG-based implicit large eddy simulations seems infeasible due to convergence issues.
Mortar methods have recently been shown to be well suited for isogeometric analysis. We review the recent mathematical analysis and then investigate the variational crime introduced by quadrature formulas for the coup...
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ISBN:
(数字)9783319233154
ISBN:
(纸本)9783319233154;9783319233147
Mortar methods have recently been shown to be well suited for isogeometric analysis. We review the recent mathematical analysis and then investigate the variational crime introduced by quadrature formulas for the coupling integrals. Motivated by finite element observations, we consider on the interface a quadrature rule purely based on the slave mesh as well as a method using on the interface quadrature rules based on the slave mesh and on the master mesh, resulting in a non-symmetric saddle point problem. While in the first case reduced convergence rates can be observed, in the second case the influence of the variational crime is less significant.
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