References
- Takizawa K, Tezduyar TE, Hattori H. Computational analysis of flow-driven string dynamics in turbomachinery. Comput Fluids. 2017;142:109–117. doi: 10.1016/j.compfluid.2016.02.019
- Pierret S, Van den Braembussche R. Turbomachinery blade design using a Navier-Stokes solver and artificial neural network. VKI Lecture Series. 1997;5:21–25.
- Dixon SL, Hall C. Fluid mechanics and thermodynamics of turbomachinery. Oxford: Elsevier Press; 2013.
- Schlichting H, Gersten K. Boundary-layer theory. Berlin: Springer-Verlag; 2016.
- O'neill B. Semi-Riemannian geometry with applications to relativity. Cambridge: Academic Press; 1983.
- Brandvik T, Pullan G. An accelerated 3D Navier-Stokes solver for flows in turbomachines. J Turbomach. 2011;133(2):021025. (9pp). doi: 10.1115/1.4001192
- Zhang J, Zhang K, Li J, et al. A weak Galerkin finite element method for the Navier–Stokes equations. Commun Comput Phys. 2018;23:706–746.
- Li Y, Li K. Existence of the solution to stationary Navier-Stokes equations with nonlinear slip boundary conditions. J Math Anal Appl. 2011;381(1):1–9. doi: 10.1016/j.jmaa.2011.04.020
- Girault V, Raviart PA. Finite element methods for Navier-Stokes equations: theory and algorithms. Berlin: Springer-Verlag; 2012.
- Zhang J, Zhang K, Li J, et al. A weak Galerkin method for diffraction gratings. Appl Anal. 2017;96(2):190–214. doi: 10.1080/00036811.2015.1118625
- Li K, Huang A. Navier-Stokes boundary shape control, dimension splitting method and its application. Beijing: Science Press; 2013.
- Ciarlet PG. An introduction to differential geometry with applications to elasticity. J Elasticty. 2005;78(1–3):1–215.
- Berger M, Gostiaux B. Differential geometry: manifolds, curves, and surfaces. New York: Springer Science & Business Media; 2012.