Energy stable boundary conditions for the nonlinear incompressible Navier-Stokes equations

The nonlinear incompressible Navier-Stokes equations with boundary conditions at far fields and solid walls is considered. Two different formulations of boundary conditions are derived using the en ...

[1]  Albert Gyr,et al.  Diffusion and transport of pollutants in atmospheric mesoscale flow fields , 1995 .

[2]  H. Kreiss,et al.  Initial-Boundary Value Problems and the Navier-Stokes Equations , 2004 .

[3]  Rolf Rannacher,et al.  ARTIFICIAL BOUNDARIES AND FLUX AND PRESSURE CONDITIONS FOR THE INCOMPRESSIBLE NAVIER–STOKES EQUATIONS , 1996 .

[4]  Alan Shapiro The Use of an Exact Solution of the Navier–Stokes Equations in a Validation Test of a Three-Dimensional Nonhydrostatic Numerical Model , 1993 .

[5]  Sinisa Krajnovic,et al.  Large-Eddy Simulation of the Flow Around Simplified Car Model , 2004 .

[6]  Per Lötstedt,et al.  High order accurate solution of the incompressible Navier-Stokes equations , 2005 .

[7]  Suchuan Dong,et al.  A robust and accurate outflow boundary condition for incompressible flow simulations on severely-truncated unbounded domains , 2014, J. Comput. Phys..

[8]  B. Christer V. Johansson Boundary conditions for open boundaries for the incompressible Navier-Stokes equation , 1993 .

[9]  J. Nordström,et al.  Summation by Parts Operators for Finite Difference Approximations of Second-Derivatives with Variable Coefficients , 2004, Journal of Scientific Computing.

[10]  Antony Jameson,et al.  Energy Stable Flux Reconstruction Schemes for Advection–Diffusion Problems on Tetrahedra , 2013, Journal of Scientific Computing.

[11]  Douglas N. Arnold,et al.  Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems , 2001, SIAM J. Numer. Anal..

[12]  P. Moin,et al.  Application of a Fractional-Step Method to Incompressible Navier-Stokes Equations , 1984 .

[13]  Jing Gong,et al.  A stable and conservative high order multi-block method for the compressible Navier-Stokes equations , 2009, J. Comput. Phys..

[14]  Jason E. Hicken,et al.  Interior Penalties for Summation-by-Parts Discretizations of Linear Second-Order Differential Equations , 2016, J. Sci. Comput..

[15]  C. Hirsch,et al.  Numerical Computation of Internal and External Flows. By C. HIRSCH. Wiley. Vol. 1, Fundamentals of Numerical Discretization. 1988. 515 pp. £60. Vol. 2, Computational Methods for Inviscid and Viscous Flows. 1990, 691 pp. £65. , 1991, Journal of Fluid Mechanics.

[16]  Malte Braack,et al.  DIRECTIONAL DO-NOTHING CONDITION FOR THE NAVIER-STOKES EQUATIONS , 2014 .

[17]  Nail K. Yamaleev,et al.  Discretely conservative finite-difference formulations for nonlinear conservation laws in split form: Theory and boundary conditions , 2013, J. Comput. Phys..

[18]  Philipp Öffner,et al.  Summation-by-parts operators for correction procedure via reconstruction , 2015, J. Comput. Phys..

[19]  Magnus Svärd,et al.  A stable high-order finite difference scheme for the compressible Navier-Stokes equations, far-field boundary conditions , 2007, J. Comput. Phys..

[20]  Jan Nordström,et al.  On conservation and stability properties for summation-by-parts schemes , 2017, J. Comput. Phys..

[21]  B. Strand Summation by parts for finite difference approximations for d/dx , 1994 .

[22]  Jan Nordström,et al.  Finite volume methods, unstructured meshes and strict stability for hyperbolic problems , 2003 .

[23]  Jan Nordström,et al.  Summation-by-parts in time , 2013, J. Comput. Phys..

[24]  Jan Nordström,et al.  Boundary conditions for a divergence free velocity-pressure formulation of the Navier-Stokes equations , 2007, J. Comput. Phys..

[25]  David Gottlieb,et al.  Spectral Methods on Arbitrary Grids , 1995 .

[26]  A. Quarteroni,et al.  On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels , 2001 .

[27]  Wendy Kress,et al.  Boundary conditions and estimates for the linearized Navier-Stokes equations on staggered grids , 2003 .

[28]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[29]  Jan Nordström,et al.  Conservative Finite Difference Formulations, Variable Coefficients, Energy Estimates and Artificial Dissipation , 2006, J. Sci. Comput..

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

[31]  Gregor Gassner,et al.  A Skew-Symmetric Discontinuous Galerkin Spectral Element Discretization and Its Relation to SBP-SAT Finite Difference Methods , 2013, SIAM J. Sci. Comput..

[32]  N. SIAMJ.,et al.  WELL-POSED BOUNDARY CONDITIONS FOR THE NAVIER – STOKES EQUATIONS , 2005 .

[33]  John C. Strikwerda,et al.  The Accuracy of the Fractional Step Method , 1999, SIAM J. Numer. Anal..

[34]  Steven H. Frankel,et al.  Entropy Stable Spectral Collocation Schemes for the Navier-Stokes Equations: Discontinuous Interfaces , 2014, SIAM J. Sci. Comput..

[35]  S. Cavadias,et al.  Analysis of Mechanisms at the Plasma–Liquid Interface in a Gas–Liquid Discharge Reactor Used for Treatment of Polluted Water , 2009 .

[36]  David W. Zingg,et al.  High-Order Implicit Time-Marching Methods Based on Generalized Summation-By-Parts Operators , 2014, SIAM J. Sci. Comput..

[37]  Bertil Gustafsson,et al.  Boundary Conditions and Estimates for the Steady Stokes Equations on Staggered Grids , 2000, J. Sci. Comput..

[38]  Jan Nordström,et al.  The use of characteristic boundary conditions for the Navier-Stokes equations , 1995 .

[39]  Jan Nordström,et al.  A Roadmap to Well Posed and Stable Problems in Computational Physics , 2016, Journal of Scientific Computing.

[40]  Magnus Svärd,et al.  Review of summation-by-parts schemes for initial-boundary-value problems , 2013, J. Comput. Phys..

[41]  L. Perelman,et al.  A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers , 1997 .

[42]  Jan Nordström,et al.  A new high order energy and enstrophy conserving Arakawa-like Jacobian differential operator , 2015, J. Comput. Phys..

[43]  William D. Henshaw,et al.  A Fourth-Order Accurate Method for the Incompressible Navier-Stokes Equations on Overlapping Grids , 1994 .

[44]  R. Glowinski,et al.  FINITE ELEMENT METHODS FOR NAVIER-STOKES EQUATIONS , 1992 .

[45]  Magnus Svärd,et al.  A stable high-order finite difference scheme for the compressible Navier-Stokes equations: No-slip wall boundary conditions , 2008, J. Comput. Phys..

[46]  N. Anders Petersson,et al.  Stability of pressure boundary conditions for Stokes and Navier-Stokes equations , 2001 .

[47]  Dan S. Henningson,et al.  The Fringe Region Technique and the Fourier Method Used in the Direct Numerical Simulation of Spatially Evolving Viscous Flows , 1999, SIAM J. Sci. Comput..

[48]  David C. Del Rey Fernández,et al.  Multidimensional Summation-by-Parts Operators: General Theory and Application to Simplex Elements , 2015, SIAM J. Sci. Comput..

[49]  P. Gresho Some current CFD issues relevant to the incompressible Navier-Stokes equations , 1991 .

[50]  David C. Del Rey Fernández,et al.  Simultaneous Approximation Terms for Multi-dimensional Summation-by-Parts Operators , 2016, J. Sci. Comput..

[51]  Thomas J. R. Hughes,et al.  Finite element modeling of blood flow in arteries , 1998 .

[52]  Jan Nordström,et al.  Weak and strong wall boundary procedures and convergence to steady-state of the Navier-Stokes equations , 2012, J. Comput. Phys..

[53]  Jan S. Hesthaven,et al.  A Stable Penalty Method for the Compressible Navier-Stokes Equations: I. Open Boundary Conditions , 1996, SIAM J. Sci. Comput..

[54]  Jan Nordström,et al.  The SBP-SAT technique for initial value problems , 2014, J. Comput. Phys..

[55]  Gregor Gassner,et al.  An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry , 2015, J. Comput. Phys..

[56]  Geoffrey K. Vallis,et al.  Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation , 2017 .

[57]  H. T. Huynh,et al.  A Flux Reconstruction Approach to High-Order Schemes Including Discontinuous Galerkin Methods , 2007 .