A deep learning framework for derivation of time-stable difference schemes

[1]  Paul E. Dimotakis,et al.  Mixing, scalar boundedness, and numerical dissipation in large-eddy simulations , 2018, J. Comput. Phys..

[2]  Daniel Livescu,et al.  Turbulence structure behind the shock in canonical shock–vortical turbulence interaction , 2014, Journal of Fluid Mechanics.

[3]  P. Moin,et al.  Suitability of upwind-biased finite difference schemes for large-eddy simulation of turbulent flows , 1997 .

[4]  Daniel J. Bodony,et al.  Energy stable overset grid methods for hyperbolic problems , 2014 .

[5]  Daniel J. Bodony,et al.  Direct numerical simulation of human phonation , 2016 .

[6]  Peter Brady,et al.  Foundations for high-order, conservative cut-cell methods: Stable discretizations on degenerate meshes , 2020, J. Comput. Phys..

[7]  Carlos Pantano,et al.  Time-stable overset grid method for hyperbolic problems using summation-by-parts operators , 2018, J. Comput. Phys..

[8]  Bolei Zhou,et al.  Interpreting the Latent Space of GANs for Semantic Face Editing , 2019, 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[9]  Bertil Gustafsson,et al.  The convergence rate for difference approximations to general mixed initial boundary value problems , 1981 .

[10]  T. Colonius,et al.  Computational aeroacoustics: progress on nonlinear problems of sound generation , 2004 .

[11]  P. Brady,et al.  High-order, stable, and conservative boundary schemes for central and compact finite differences , 2017, Computers & Fluids.

[12]  P. Moin,et al.  Fully Conservative Higher Order Finite Difference Schemes for Incompressible Flow , 1998 .

[13]  Bolei Zhou,et al.  Semantic Hierarchy Emerges in Deep Generative Representations for Scene Synthesis , 2019, ArXiv.

[14]  Parviz Moin,et al.  Direct simulations of turbulent flow using finite-difference schemes , 1991 .

[15]  P. Dimotakis,et al.  Turbulent shear-layer mixing: initial conditions, and direct-numerical and large-eddy simulations , 2019, Journal of Fluid Mechanics.

[16]  Christopher K. W. Tam,et al.  Wall boundary conditions for high-order finite-difference schemes in computational aeroacoustics , 1994 .

[17]  B. Gustafsson.  The convergence rate for difference approximations to mixed initial boundary value problems , 1975 .

[18]  Ruslan Salakhutdinov,et al.  Learning Deep Generative Models , 2009 .

[19]  Martin Corless,et al.  Linear systems and control : an operator perspective , 2003 .

[20]  D. Bodony,et al.  Global mode-based control of laminar and turbulent high-speed jets , 2018, Comptes Rendus Mécanique.

[21]  L. Trefethen.  Stability of finite difference models containing two boundaries or interfaces , 1985 .

[22]  D. Gottlieb,et al.  Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: methodology and application to high-order compact schemes , 1994 .