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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
document
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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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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