FDL3DI swMATH ID: 24948 Software Authors: Gaitonde, Datta V.; Visbal, Miguel R. Description: High-Order Schemes for Navier-Stokes Equations: Algorithm and Implementation Into FDL3DI. A spectrum of higher-order schemes is developed to solve the Navier-Stokes equations in finite-difference formulations. Pade type formulas of up to sixth order with a five-point stencil are developed for the difference scheme. Viscous terms are treated by successive applications of the first derivative operator. However, formulas are also derived for use in a mid-point interpolation-differentiation strategy. For numerical stability, up to tenth-order filtering schemes are developed. The spectral properties of the differentiation and filtering schemes are examined and guidelines are provided to choose proper filter coefficients. Special high-order formulas are obtained for differentiation and filtering in the vicinity of boundaries. The coefficients required for systematic implementation of Neumann-type boundary conditions are also presented. A brief description is provided of the manner in which the FDL3DI code is enhanced by coupling the approximately-factored procedure with these compact-difference based algorithms and by incorporating an explicit fourth-order Runge-Kutta scheme. Homepage: http://www.dtic.mil/docs/citations/ADA364301 Related Software: XFOIL; MPI; SOLA; HE-E1GODF; HIGAN; DGM; AlexNet; PDE-Net; Adam; ImageNet; PyTorch; Keras; TensorFlow; NumPy; AABB; CGAL; MOOD; PETSc; MersenneTwister; OVERFLOW 2 Cited in: 56 Publications all top 5 Cited by 97 Authors 14 Visbal, Miguel R. 9 Rizzetta, Donald P. 7 Gaitonde, Datta V. 4 Gürarslan, Gürhan 4 Sarı, Murat 3 Colominas, Ignasi 3 Lele, Sanjiva K. 3 Li, Jichun 3 Nogueira, Xesús 2 Adler, Michael C. 2 Cueto-Felgueroso, Luis 2 Kampanis, Nikolaos A. 2 Kawai, Soshi 2 Shankar, Santhosh K. 2 Shi, Yufeng 2 Xu, Biao 1 Aragon-Calvo, Miguel A. 1 Asai, Masahito 1 Balachandar, S. Raja 1 Barnes, C. J. 1 Bellan, Josette 1 Bhagatwala, Ankit V. 1 Bisek, Nicholas J. 1 Blaisdell, Gregory A. 1 Cabot, William H. 1 Cai, Xiaodan 1 Chen, Shiyi 1 Chen, Yitung 1 Da, Dris 1 Delis, Argiris I. 1 Desjardins, Olivier 1 Ekaterinaris, John A. 1 El-Azab, M. S. 1 Emerson, David R. 1 Fernández-Fidalgo, Javier 1 Fico, Vincenzo 1 Fiorina, Benoît 1 Garmann, Daniel J. 1 Gibou, Frédéric 1 Gómez, Héctor J. 1 Gonzalez, David R. 1 Gosse, Ryan 1 Ha, Sanghyun 1 Hammad, D. A. 1 Hammer, Patrick R. 1 Haselbacher, Andreas 1 Hawkes, Evatt R. 1 Huang, Pingan 1 Inasawa, Ayumu 1 Jeong, Jaeyong 1 Johnsen, Eric 1 Khelladi, Sofiane 1 Khosla, Prem K. 1 Koochesfahani, Manoochehr M. 1 Kozyrakis, G. V. 1 Kuhn, Michael B. 1 Ladeinde, Foluso 1 Larsson, Johan 1 Li, Qin 1 Liu, Guoqing 1 Liu, Pengxin 1 Lyrintzis, Anastasios S. 1 Mistani, Pouria A. 1 Moin, Parviz 1 Morgan, P. E. 1 Motheau, Emmanuel 1 Naguib, Ahmed M. 1 Nakano, Takuya 1 Olson, Britton J. 1 Pakravan, Samira 1 Pitsch, Heinz 1 Poggie, Jonathan 1 Ramirez, Luis J. 1 Ranadive, Harshad D. 1 Rawat, Pradeep Singh 1 Reese, Jason M. 1 Rubin, Stanley G. 1 Rumpfkeil, Markus P. 1 Savard, Bruno 1 Scott, James N. 1 Sherer, Scott E. 1 Shi, Yipeng 1 Sjogreen, Bjorn 1 Stack, Cory M. 1 Stanek, Michael J. 1 Sun, Dong 1 Terashima, Hiroshi 1 Toki, Takahiko 1 Tsoutsanis, Panagiotis 1 Wan, Minping 1 Wang, Haiou 1 White, Michael D. 1 Yang, Kun 1 Yang, Yan 1 Yee, Helen C. 1 You, Donghyun 1 Zhong, Xiaolin all top 5 Cited in 16 Serials 15 Journal of Computational Physics 10 Computers and Fluids 8 International Journal of Computational Fluid Dynamics 4 Journal of Fluid Mechanics 4 Applied Mathematics and Computation 2 Computer Methods in Applied Mechanics and Engineering 2 International Journal for Numerical Methods in Fluids 2 Applied Numerical Mathematics 2 Journal of Scientific Computing 1 Computers & Mathematics with Applications 1 Numerical Methods for Partial Differential Equations 1 Mathematical Problems in Engineering 1 Abstract and Applied Analysis 1 Advances in Difference Equations 1 Communications in Computational Physics 1 International Journal for Numerical Methods in Biomedical Engineering all top 5 Cited in 9 Fields 44 Fluid mechanics (76-XX) 26 Numerical analysis (65-XX) 14 Partial differential equations (35-XX) 4 Classical thermodynamics, heat transfer (80-XX) 2 Optics, electromagnetic theory (78-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Computer science (68-XX) 1 Mechanics of deformable solids (74-XX) 1 Geophysics (86-XX) Citations by Year