1@article{arruda1993largestretch, 2 title = {A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials}, 3 author = {Arruda, Ellen M and Boyce, Mary C}, 4 journal = {Journal of the Mechanics and Physics of Solids}, 5 volume = {41}, 6 number = {2}, 7 pages = {389--412}, 8 year = {1993}, 9 publisher = {Elsevier}, 10 doi = {10.1016/0022-5096(93)90013-6} 11} 12 13@book{belytschko2013nonlinear, 14 title = {Nonlinear finite elements for continua and structures}, 15 author = {Belytschko, Ted and Liu, Wing Kam and Moran, Brian and Elkhodary, Khalil}, 16 year = {2013}, 17 publisher = {John wiley \& sons} 18} 19 20@article{brown2010, 21 adsurl = {https://doi.org/10.1007/s10915-010-9396-8}, 22 author = {{Brown}, J.}, 23 journal = {Journal of Scientific Computing}, 24 volume = 45, 25 month = oct, 26 title = {{Efficient Nonlinear Solvers for Nodal High-Order Finite Elements in 3D}}, 27 year = 2010, 28 doi = {10.1007/s10915-010-9396-8} 29} 30 31@article{giraldoetal2010, 32 author = {Giraldo, F. X. and Restelli, M. and Läuter, M.}, 33 title = {Semi-Implicit Formulations of the Navier–Stokes Equations: Application to Nonhydrostatic Atmospheric Modeling}, 34 journal = {SIAM Journal on Scientific Computing}, 35 volume = {32}, 36 number = {6}, 37 pages = {3394--3425}, 38 year = {2010}, 39 doi = {10.1137/090775889} 40} 41 42@book{holzapfel2000nonlinear, 43 author = {Holzapfel, Gerhard}, 44 title = {Nonlinear solid mechanics: a continuum approach for engineering}, 45 publisher = {Wiley}, 46 year = {2000}, 47 address = {Chichester New York}, 48 isbn = {978-0-471-82319-3} 49} 50 51@article{hughesetal2010, 52 title = {Stabilized Methods for Compressible Flows}, 53 author = {Hughes, Thomas J R and Scovazzi, Guglielmo and Tezduyar, Tayfun E}, 54 journal = {Journal of Scientific Computing}, 55 volume = {43}, 56 pages = {343--368}, 57 year = {2010}, 58 doi = {10.1007/s10915-008-9233-5} 59} 60 61@book{hughes2012finite, 62 title = {The finite element method: linear static and dynamic finite element analysis}, 63 author = {Hughes, Thomas JR}, 64 year = {2012}, 65 publisher = {Courier Corporation} 66} 67 68@article{libceed-joss-paper, 69 author = {Jed Brown and Ahmad Abdelfattah and Valeria Barra and Natalie Beams and Jean Sylvain Camier and Veselin Dobrev and Yohann Dudouit and Leila Ghaffari and Tzanio Kolev and David Medina and Will Pazner and Thilina Ratnayaka and Jeremy Thompson and Stan Tomov}, 70 title = {{libCEED}: Fast algebra for high-order element-based discretizations}, 71 journal = {Journal of Open Source Software}, 72 year = {2021}, 73 publisher = {The Open Journal}, 74 volume = {6}, 75 number = {63}, 76 pages = {2945}, 77 doi = {10.21105/joss.02945} 78} 79 80@article{papanastasiou1992outflow, 81 title = {A new outflow boundary condition}, 82 author = {Papanastasiou, TC and Malamataris, N and Ellwood K}, 83 year = {1992}, 84 month = mar, 85 pages = {587--608}, 86 volume = {14}, 87 journal = {International Journal for Numerical Methods in Fluids}, 88 doi = {10.1002/fld.1650140506} 89} 90 91@article{straka1993numerical, 92 title = {Numerical solutions of a non-linear density current: A benchmark solution and comparisons}, 93 author = {Straka, Jerry M and Wilhelmson, Robert B and Wicker, Louis J and Anderson, John R and Droegemeier, Kelvin K}, 94 journal = {International Journal for Numerical Methods in Fluids}, 95 volume = {17}, 96 number = {1}, 97 pages = {1--22}, 98 year = {1993}, 99 publisher = {Wiley Online Library}, 100 doi = {10.1002/fld.1650170103} 101} 102 103@article{williams2009roofline, 104 title = {Roofline: an insightful visual performance model for multicore architectures}, 105 author = {Williams, Samuel and Waterman, Andrew and Patterson, David}, 106 journal = {Communications of the ACM}, 107 volume = {52}, 108 number = {4}, 109 pages = {65--76}, 110 year = {2009}, 111 publisher = {ACM New York, NY, USA}, 112 doi = {10.1145/1498765.1498785} 113} 114 115@article{davydov2020matrix, 116 title = {A matrix-free approach for finite-strain hyperelastic problems using geometric multigrid}, 117 author = {Davydov, Denis and Pelteret, Jean-Paul and Arndt, Daniel and Kronbichler, Martin and Steinmann, Paul}, 118 journal = {International Journal for Numerical Methods in Engineering}, 119 volume = {121}, 120 number = {13}, 121 pages = {2874--2895}, 122 year = {2020}, 123 publisher = {Wiley Online Library}, 124 doi = {10.1002/nme.6336} 125} 126 127@article{zhang2011verification, 128 title = {On the Order of Accuracy and Numerical Performance of Two Classes of Finite Volume WENO Schemes}, 129 author = {Zhang, Rui and Zhang, Mengping and Shu, Chi-Wang}, 130 volume = {9}, 131 doi = {10.4208/cicp.291109.080410s}, 132 number = {3}, 133 journal = {Communications in Computational Physics}, 134 publisher = {Cambridge University Press}, 135 year = {2011}, 136 pages = {807--827} 137} 138 139@book{bower2010applied, 140 title = {Applied mechanics of solids}, 141 author = {Bower, Allan F}, 142 year = {2010}, 143 publisher = {CRC press}, 144 isbn = {978-1-4398-0247-2} 145} 146 147@article{whiting2003hierarchical, 148 title = {Hierarchical basis for stabilized finite element methods for compressible flows}, 149 author = {Whiting, Christian H and Jansen, Kenneth E and Dey, Saikat}, 150 journal = {Computer Methods in Applied Mechanics and Engineering}, 151 volume = {192}, 152 number = {47-48}, 153 pages = {5167--5185}, 154 year = {2003}, 155 publisher = {Elsevier}, 156 doi = {10.1016/j.cma.2003.07.011} 157} 158 159@book{toro2009, 160 title = {Riemann Solvers and Numerical Methods for Fluid Dynamics}, 161 author = {Toro, Eleuterio F.}, 162 year = {2009}, 163 publisher = {Springer, Berlin, Heidelberg}, 164 isbn = {978-3-540-49834-6} 165} 166 167@misc{sodshocktubewiki, 168 title = {Sod shock tube}, 169 howpublished = {\url{https://en.wikipedia.org/wiki/Sod_shock_tube}}, 170 note = {Accessed: 01-30-2022} 171} 172 173@article{tezduyar2007yzb, 174 title = {{SUPG} finite element computation of inviscid supersonic flows with $YZ\beta$ shock capturing}, 175 author = {Tezduyar, Tayfun E and Senga, Masayoshi}, 176 journal = {Computers and Fluids}, 177 volume = {36}, 178 number = {1}, 179 pages = {147-159}, 180 year = {2007}, 181 publisher = {Elsevier}, 182 doi = {10.1016/j.compfluid.2005.07.009} 183} 184 185@phdthesis{whitingStabilizedFEM1999, 186 title = {Stabilized {{Finite Element Methods}} for {{Fluid Dynamics}} Using a {{Hierarchical Basis}}}, 187 author = {Whiting, Christian H}, 188 year = {1999}, 189 address = {{Troy, NY}}, 190 langid = {english}, 191 school = {Rennselear Polytechnic Institute} 192} 193 194@article{shurSTG2014, 195 title = {Synthetic Turbulence Generators for {RANS-LES} Interfaces in Zonal Simulations of Aerodynamic and Aeroacoustic Problems}, 196 author = {Shur, Michael L. and Spalart, Philippe R. and Strelets, Michael K. and Travin, Andrey K.}, 197 year = {2014}, 198 journal = {Flow, Turbulence and Combustion}, 199 volume = {93}, 200 number = {1}, 201 pages = {63--92}, 202 doi = {10.1007/s10494-014-9534-8}, 203 langid = {english} 204} 205 206@inproceedings{mengaldoCompressibleBC2014, 207 title = {A Guide to the Implementation of Boundary Conditions in Compact High-Order Methods for Compressible Aerodynamics}, 208 booktitle = {{{AIAA Aviation}} 2014}, 209 author = {Mengaldo, Gianmarco and De Grazia, Daniele and Peiro, Joaquim and Farrington, Antony and Witherden, Freddie and Vincent, Peter and Sherwin, Spencer}, 210 year = {2014}, 211 month = jun, 212 publisher = {{AIAA}}, 213 address = {{Atlanta}}, 214 doi = {10.2514/6.2014-2923} 215} 216 217@article{shakib1991femcfd, 218 title = {A new finite element formulation for computational fluid dynamics: {X}. The compressible {Euler} and {Navier-Stokes} equations}, 219 author = {Shakib, Farzin and Hughes, Thomas JR and Johan, Zden{\v{e}}k}, 220 journal = {Computer Methods in Applied Mechanics and Engineering}, 221 volume = {89}, 222 number = {1-3}, 223 pages = {141--219}, 224 year = {1991}, 225 publisher = {Elsevier}, 226 doi = {10.1016/0045-7825(91)90041-4} 227} 228