Bibliography

[1]

David A. Kopriva and Gregor Gassner. On the quadrature and weak form choices in collocation type discontinuous galerkin spectral element methods. Journal of Scientific Computing, 44:136–155, 2010.

[2]

Florian Hindenlang, Gregor J Gassner, Christoph Altmann, Andrea Beck, Marc Staudenmaier, and Claus-Dieter Munz. Explicit discontinuous galerkin methods for unsteady problems. Computers & Fluids, 61:86–93, 2012.

[3]

Matthias Sonntag and Claus-Dieter Munz. Efficient parallelization of a shock capturing for discontinuous galerkin methods using finite volume sub-cells. Journal of Scientific Computing, 70(3):1262–1289, 2017.

[4]

Sebastian Hennemann, Andrés M Rueda-Ramírez, Florian J Hindenlang, and Gregor J Gassner. A provably entropy stable subcell shock capturing approach for high order split form dg for the compressible euler equations. Journal of Computational Physics, 426:109935, 2021.

[5]

M. Carpenter and C. Kennedy. Fourth-order 2N-storage Runge-Kutta schemes. Technical Report NASA TM 109111, Langley Research Center, Hampton, Virginia, 1994.

[6]

Jens Niegemann, Richard Diehl, and Kurt Busch. Efficient low-storage runge–kutta schemes with optimized stability regions. Journal of Computational Physics, 231(2):364–372, 2012.

[7]

David A Kopriva, Stephen L Woodruff, and M Yousuff Hussaini. Computation of electromagnetic scattering with a non-conforming discontinuous spectral element method. International journal for numerical methods in engineering, 53(1):105–122, 2002.

[8]

David Flad, Hannes Frank, Andrea D Beck, and Claus-Dieter Munz. A discontinuous galerkin spectral element method for the direct numerical simulation of aeroacoustics. In 20th AIAA/CEAS Aeroacoustics Conference, 2740. 2014.

[9]

Jan-Reneé Carlson. Inflow/outflow boundary conditions with application to fun3d. Technical Report, Langley Research Center, Hampton, Virginia, 2011.

[10]

Gregor J. Gassner, Andrew R. Winters, and David A. Kopriva. Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations. J. Comput. Phys., 327:39–66, December 2016. doi:10.1016/j.jcp.2016.09.013.

[11]

Gregor J Gassner and Andrea D Beck. On the accuracy of high-order discretizations for underresolved turbulence simulations. Theoretical and Computational Fluid Dynamics, 27(3-4):221–237, 2013.

[12]

F. Bassi and S. Rebay. A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. J. Comput. Phys., 131:267–279, 1997.

[13]

F. Bassi, S. Rebay, G. Mariotti, S. Pedinotti, and M. Savini. A high-order accurate discontinuous finite element method fir inviscid an viscous turbomachinery flows. In R. Decuypere and G. Dibelius, editors, Proceedings of 2nd European Conference on Turbomachinery, Fluid and Thermodynamics, 99–108. Technologisch Instituut, Antwerpen, Belgium, 1997.

[14]

Sergio Pirozzoli. Generalized conservative approximations of split convective derivative operators. Journal of Computational Physics, 229:7180–7190, 2010.

[15]

Praveen Chandrashekar. Kinetic energy preserving and entropy stable finite volume schemes for compressible euler and navier-stokes equations. Communications in Computational Physics, 14:1252–1286, 2013.

[16]

Marcel Blind, Min Gao, Daniel Kempf, Patrick Kopper, Marius Kurz, Anna Schwarz, and Andrea Beck. Towards exascale cfd simulations using the discontinuous galerkin solver flexi. In High Performance Computing in Science and Engineering '23 (in press). 2024.

[17]

Gregor Gassner and David A Kopriva. A comparison of the dispersion and dissipation errors of gauss and gauss–lobatto discontinuous galerkin spectral element methods. SIAM Journal on Scientific Computing, 33(5):2560–2579, 2011.

[18]

Patrick J. Roache. Code Verification by the Method of Manufactured Solutions. Journal of Fluids Engineering, 124(1):4–10, November 2001.

[19]

UKNG Ghia, Kirti N Ghia, and CT Shin. High-re solutions for incompressible flow using the navier-stokes equations and a multigrid method. Journal of computational physics, 48(3):387–411, 1982.

[20]

Zhen Gao, Jan S. Hesthaven, and Tim Warburton. Efficient absorbing layers for weakly compressible flows. 2016. URL: https://infoscience.epfl.ch/handle/20.500.14299/97200.

[21]

Geoffrey Ingram Taylor and Albert Edward Green. Mechanism of the production of small eddies from large ones. Proceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences, 158(895):499–521, February 1937. doi:10.1098/rspa.1937.0036.

[22]

Gary A Sod. A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. Journal of computational physics, 27(1):1–31, 1978.

[23]

Per-Olof Persson and Jaime Peraire. Sub-Cell Shock Capturing for Discontinuous Galerkin Methods. In Proceedings of the 44th AIAA Aerospace Sciences Meeting and Exhibit. American Institute of Aeronautics and Astronautics, 2006. doi:10.2514/6.2006-112.

[24]

Phillip Colella and Paul R Woodward. The piecewise parabolic method (ppm) for gas-dynamical simulations. Journal of computational physics, 54(1):174–201, 1984.

[25]

Antony Jameson, Wolfgang Schmidt, and Eli Turkel. Numerical solution of the euler equations by finite volume methods using runge kutta time stepping schemes. In 14th fluid and plasma dynamics conference, 1259. 1981.

[26]

Robert D Moser, John Kim, and Nagi N Mansour. Direct numerical simulation of turbulent channel flow up to reτ= 590. Physics of fluids, 11(4):943–945, 1999.

[27]

J. Smagorinsky. General circulation experiments with the primitive equations. Monthly Weather Review, 91(3):99–164, March 1963. doi:10.1175/1520-0493(1963)091<0099:gcewtp>2.3.co;2.

[28]

Peter J Schmid, Knud Erik Meyer, and Oliver Pust. Dynamic mode decomposition and proper orthogonal decomposition of flow in a lid-driven cylindrical cavity. In 8th International Symposium on Particle Image Velocimetry, 25–28. 2009.

[29]

Xiangxiong Zhang and Chi-Wang Shu. On positivity-preserving high order discontinuous galerkin schemes for compressible euler equations on rectangular meshes. Journal of Computational Physics, 229(23):8918–8934, 2010. doi:10.1016/j.jcp.2010.08.016.