TY - THES A1 - Kemm, Friedemann T1 - Divergenzkorrekturen und asymptotische Untersuchungen bei der numerischen Simulation idealer magnetohydrodynamischer Strömungen Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bsz:93-opus-27335 CY - Stuttgart ER - TY - JOUR A1 - Kemm, Friedemann T1 - Magnetische Ladungen oder, warum es manchmal sinnvoll ist, etwas mathematisch zu modellieren, was es gar nicht gibt Y1 - 2006 UR - http://www.springerlink.de/content/ag63461567j42331/?p=70a9b1cfc3224a11b74f9a373d00697f&pi=1 ER - TY - CHAP A1 - Kemm, Friedemann A1 - Lee, Yong-Joong A1 - Schneider, Rudolf T1 - Hyperbolic GLM scheme for elliptic constraints in computational electromagnetics and MHD Y1 - 2005 ER - TY - CHAP A1 - Kemm, Friedemann ED - Tadmor, Eitan T1 - Discrete Involutions, Resonance, and the Divergence Problem in MHD T2 - Hyperbolic problems, proceedings of the 12th international conference on hyperbolic problems, June 9-13, 2008 Y1 - 2009 SN - 978-0-8218-4730-5 SN - 978-0-8218-4728-2 SP - 725 EP - 735 PB - American Mathematical Society CY - Providence, RI ER - TY - GEN A1 - Kemm, Friedemann T1 - A comparative study of TVD limiters - well known limiters and an introduction of new ones T2 - International Journal for Numerical methods in Fluids N2 - This paper gives a comparative study of TVD-limiters for standard explicit Finite Volume schemes. In contrast to older studies it includes also unsymmetrical limiter functions which depend on the local CFL-number. We classify the limiters and show how to extend these families of limiters. We introduce a new member of the Superbee family, which is adapted to Roe's linear third-order scheme. Based on an idea by Serna and Marquina, new smooth limiters are introduced, which turn the van~Leer and van~Albada limiters into complete classes of limiters. The comparison of the limiters is done with some standard test cases. The results clarify the influence of the chosen limiter on the quality of the numerical results. Compared to ENO or WENO schemes, they also show the high resolution, which can be obtained by a CFL-number dependent limiter when the grid is not highly refined. KW - total variation diminishing KW - finite volumes KW - limiter Y1 - 2011 UR - http://onlinelibrary.wiley.com/doi/10.1002/fld.2357/abstract;jsessionid=CB2EEF03FA7F60EC2462A289F8C3E5DE.d01t02?deniedAccessCustomisedMessage=&userIsAuthenticated=false U6 - https://doi.org/10.1002/fld.2357 VL - 67 IS - 4 SP - 404 EP - 440 ER - TY - THES A1 - Kemm, Friedemann T1 - Contributions to the Numerical Simulation of Gas, Shallow Water, and Plasma Flows: Wave-wise Treatment of Order and Viscosity Y1 - 2014 ER - TY - CHAP A1 - Bader, Georg A1 - Kemm, Friedemann T1 - The carbuncle phenomenon in shallow water simulations T2 - 2nd International Conference on Computational Science and Engineering, 21-23 August 2014, Ho Chi Minh City, Vietnam N2 - The carbuncle phenomenon, an instability of discrete shock profiles, has been known in gas dynamics simulations for a long time. Only recently, it was also observed in shallow water simulations. It was shown that the mechanisms and cures in shallow water are closely related to the mechanisms and cures in gas dynamics. In this paper, we give further evidence of that and, by means of new test cases, give evidence of the strength of our HLLEMCC approach to avoid the carbuncle in shallow water. Y1 - 2014 UR - https://www.researchgate.net/publication/263845832_The_Carbuncle_Phenomenon_in_Shallow_Water_Simulations ER - TY - CHAP A1 - Kemm, Friedemann ED - Vázquez-Cendón, Elena ED - Hidalgo, Arturo ED - García-Navarro, Pilar ED - Cea, Luis T1 - CFL-Number-dependent TVD-Limiters T2 - Numerical Methods for Hyperbolic Equations: Theory and Applications N2 - In this paper, we show how algebraic limiting and limiters which take into account the local CFL-number lead to a significant increase in accuracy. Furthermore, we show how these limiters can be easily adapted to the nonlinear TVD-condition by Jeng and Payne. KW - total variation diminishing KW - finite volumes KW - limiter KW - CFL-number Y1 - 2013 SN - 978-0-415-62150-2 SP - 277 EP - 283 PB - CRC Press, Taylor & Francis Group CY - London ER - TY - GEN A1 - Kemm, Friedemann T1 - A note on the carbuncle phenomenon in shallow water simulations T2 - ZAMM‐Journal of Applied Mathematics and Mechanics N2 - A classic problem in gas dynamics simulation is the occurrence of the carbuncle phenomenon, a breakdown of discrete shock profiles. We show that for high Froude number, this also occurs in shallow water simulations. Numerical evidence is given that commonly accepted cures developed for the numerics of gas dynamics should also work for shallow water flows. Y1 - 2014 SN - 1521-4001 SN - 0044-2267 VL - 94 IS - 6 SP - 516 EP - 521 ER - TY - GEN A1 - Kemm, Friedemann T1 - On the origin of divergence errors in MHD simulations and consequences for numerical schemes T2 - Communications in Applied Mathematics and Computational Science N2 - This paper investigates the origin of divergence errors in MHD simulations. For that purpose, we introduce the concept of discrete involutions for discretized conservation laws. This is done in analogue to the concept of involutions for hyperbolic conservation laws, introduced by Dafermos. By exploring the connection between discrete involutions and resonance, especially for constrained transport like MHD, we identify the lack of positive central viscosity and the assumption of one-dimensional physics in the calculation of intercell fluxes as the main sources of divergence errors. As an example of the consequences for numerical schemes, we give a hint how to modify Roe-type schemes in order to decrease the divergence errors considerably and, thus, stabilize the scheme. KW - involutions KW - magnetohydrodynamics KW - plasma physics KW - resonance KW - hyperbolic PDE KW - finite volume method KW - finite differences Y1 - 2013 UR - http://msp.org/camcos/2013/8-1/p01.xhtml U6 - https://doi.org/10.2140/camcos.2013.8.1 SN - 2157-5452 SN - 1559-3940 VL - 8 IS - 1 SP - 1 EP - 38 ER - TY - CHAP A1 - Kemm, Friedemann ED - Benzoni-Gavage, Sylvie T1 - A carbuncle free Roe-type solver for the Euler equations T2 - Hyperbolic problems, proceedings of the Eleventh International Conference on Hyperbolic Problems, held in Ecole Normale Supérieure, Lyon, July 17 - 21, 2006 N2 - Based on the idea of the HLLEM scheme, we propose a novel ansatz to cure the well known carbuncle instability. Instead of testing all neighboring cells for strong shocks we test the Riemann problem for contact and shear waves. As an indicator we suggest the residual of the Rankine-Hugoniot condition for the linear waves. By using known approaches, we can apply a well tempered amount of viscosity for the contact and shear waves of the Roe and HLLEM methods. The resulting Riemann solver approximates contact and shear waves exactly. However, according to the chosen value of a parameter, the Carbuncle phenomenon can be completely avoided. KW - numerical examples KW - Euler equations KW - Roe method KW - HLLEM scheme KW - carbuncle instability KW - shocks KW - Riemann problem KW - contact and shear waves KW - Rankine-Hugoniot condition KW - supersonic flows Y1 - 2008 UR - http://springerlink.com/content/h46448g01h674285/fulltext.pdf SN - 3-540-75711-2 SN - 978-3-540-75711-5 SP - 601 EP - 608 PB - Springer CY - Berlin [u.a.] ER - TY - GEN A1 - Breuß, Michael A1 - Kemm, Friedemann A1 - Vogel, Oliver T1 - A numerical study of Newton interpolation with extremely high degrees T2 - Kybernetika : international journal published by Institute of Information Theory and Automation N2 - In current textbooks the use of Chebyshev nodes with Newton interpolation is advocated as the most efficient numerical interpolation method in terms of approximation accuracy and computational effort. However, we show numerically that the approximation quality obtained by Newton interpolation with Fast Leja (FL) points is competitive to the use of Chebyshev nodes, even for extremely high degree interpolation. This is an experimental account of the analytic result that the limit distribution of FL points and Chebyshev nodes is the same when letting the number of points go to infinity. Since the FL construction is easy to perform and allows to add interpolation nodes on the fly in contrast to the use of Chebyshev nodes, our study suggests that Newton interpolation with FL points is currently the most efficient numerical technique for polynomial interpolation. Moreover, we give numerical evidence that any reasonable function can be approximated up to machine accuracy by Newton interpolation with FL points if desired, which shows the potential of this method. KW - polynomial interpolation KW - Newton interpolation KW - interpolation nodes KW - Chebyshev nodes KW - Leja ordering KW - fast Leja points Y1 - 2018 U6 - https://doi.org/10.14736/kyb-2018-2-0279 SN - 0023-5954 VL - 54 IS - 2 SP - 279 EP - 288 ER -