Searched for: subject:"high%5C-order%5C+methods"
(1 - 14 of 14)
document
Vuik, M.J. (author)
This dissertation addresses practical use of multiwavelets and outlier detection for troubled-cell indication for discontinuous Galerkin (DG) methods. For smooth solutions, the DG approximation converges to the exact solution with a high order of accuracy. However, problems may arise when shock waves or discontinuities appear: non-physical...
doctoral thesis 2017
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Vuik, M.J. (author), Ryan, J.K. (author)
In Vuik and Ryan [J. Comput. Phys., 270 (2014), pp. 138--160] we studied the use of troubled-cell indicators for discontinuity detection in nonlinear hyperbolic partial differential equations and introduced a new multiwavelet technique to detect troubled cells. We found that these methods perform well as long as a suitable, problem-dependent...
journal article 2016
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King, J. (author), Mirzaee, H. (author), Ryan, J.K. (author), Kirby, R.M. (author)
Smoothness-increasing accuracy-conserving (SIAC) filtering has demonstrated its effectiveness in raising the convergence rate of discontinuous Galerkin solutions from order k + 12 to order 2k + 1 for specific types of translation invariant meshes (Cockburn et al. in Math. Comput. 72:577–606, 2003; Curtis et al. in SIAM J. Sci. Comput. 30(1):272...
journal article 2012
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Mirzaee, H. (author), Li, L. (author), Ryan, J.K. (author), Kirby, R.M. (author)
Theoretically and computationally, it is possible to demonstrate that the order of accuracy of a discontinuous Galerkin (DG) solution for linear hyperbolic equations can be improved from order $k$+1 to 2$k$+1 through the use of smoothness-increasing accuracy-conserving (SIAC) filtering. However, it is a computationally complex task to perform...
journal article 2011
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Mirzaee, H. (author), Ryan, J.K. (author), Kirby, R.M. (author)
The discontinuous Galerkin (DG) methods provide a high-order extension of the finite volume method in much the same way as high-order or spectral/hp elements extend standard finite elements. However, lack of inter-element continuity is often contrary to the smoothness assumptions upon which many post-processing algorithms such as those used in...
journal article 2011
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Van Slingerland, P. (author), Ryan, J.K. (author), Vuik, C. (author)
Position-dependent smoothness-increasing accuracy-conserving (SIAC) filtering is a promising technique not only in improving the order of the numerical solution obtained by a discontinuous Galerkin (DG) method but also in increasing the smoothness of the field and improving the magnitude of the errors. This was initially established as an...
journal article 2011
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Mirzaee, H. (author), Ryan, J.K. (author), Kirby, R.M. (author)
The discontinuous Galerkin (DG) method continues to maintain heightened levels of interest within the simulation community because of the discretization flexibility it provides. Although one of the fundamental properties of the DG methodology and arguably its most powerful property is the ability to combine high-order discretizations on an...
journal article 2010
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Walfisch, D. (author), Ryan, J.K. (author), Kirby, R.M. (author), Haimes, R. (author)
The discontinuous Galerkin (DG) method continues to maintain heightened levels of interest within the simulation community because of the discretization flexibility it provides. One of the fundamental properties of the DG methodology and arguably its most powerful property is the ability to combine high-order discretizations on an inter-element...
journal article 2008
document
Utzmann, J. (author), Munz, C.D. (author)
This paper advances the idea of a heterogeneous domain decomposition for Computational Aeroacoustics (CAA). Direct simulations of aeroacoustic problems are accelerated by sub-dividing the computational domain into smaller domains. In each of these sub-domains the equations, the discretization, the mesh and the time step may be different and are...
conference paper 2006
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Lörcher, F. (author), Gassner, G. (author), Munz, C.D. (author)
Numerical schemes for wave propagation over long distances need good wave propagation properties with low dispersion and low dissipation errors. Suitable numerical methods are methods with high order of accuracy in space and time. For space discretization on structured grids, high order finite difference schemes are efficient, and, if a...
conference paper 2006
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Hidalgo, A. (author), Toro, E.F. (author), Conde, C. (author)
Nonlinear acoustic waves have many applications in very different fields of industry. The problem considered in this work consists of predicting the behaviour of gas filling a one dimensional tube when suffering the action of very high frequency waves. The numerical technique applied to solve this problem is a third order finite volume method...
conference paper 2006
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Boersma, B.J. (author), Van der Hoeven, S. (author)
Modeling of scalar transport is an essential point in the simulation of non-premixed turbulent combustion. The fuel and oxidizer streams are, in general, modeled with an equation for the mixture fraction $Z$. This mixture fraction is a bounded function, i.e. it can never become large than one or smaller than zero. Symmetric central differencing...
conference paper 2006
document
Boersma, B.J. (author), Van der Hoeven, S. (author)
Modeling of scalar transport is an essential point in the simulation of non-premixed turbulent combustion. The fuel and oxidizer streams are, in general, modeled with an equation for the mixture fraction Z. This mixture fraction is a bounded function, i.e. it can never become large than one or smaller than zero. Symmetric central differencing...
conference paper 2006
document
Rokicki, J. (author), Wieteska, R. (author)
The paper discusses finite volume WENO reconstruction applied to simulation of compressible 3D Euler flows using unstructured tetrahedral meshes. The main point of interest is the case when the mesh becomes highly irregular or stretched. Special transformation is used in such cases to recover the third-order accuracy of reconstruction. This...
conference paper 2006
Searched for: subject:"high%5C-order%5C+methods"
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