High order time integration and mesh adaptation with error control for incompressible Navier-Stokes and scalar transport resolution on dual grids

[1]  F. Harlow,et al.  Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface , 1965 .

[2]  R. Temam.  Une méthode d'approximation de la solution des équations de Navier-Stokes , 1968 .

[3]  A. Chorin.  Numerical solution of the Navier-Stokes equations , 1968 .

[4]  A. Prothero,et al.  On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations , 1974 .

[5]  M. Berger,et al.  Adaptive mesh refinement for hyperbolic partial differential equations , 1982 .

[6]  C. Rhie,et al.  Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation , 1983 .

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

[8]  R. Sani,et al.  On pressure boundary conditions for the incompressible Navier‐Stokes equations , 1987 .

[9]  William Gropp,et al.  Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries , 1997, SciTools.

[10]  Barna L. Bihari,et al.  Multiresolution Schemes for the Numerical Solution of 2-D Conservation Laws I , 1997, SIAM J. Sci. Comput..

[11]  John B. Bell,et al.  An Adaptive Projection Method for Unsteady, Low-Mach Number Combustion , 1998 .

[12]  Uri M. Ascher,et al.  Computer methods for ordinary differential equations and differential-algebraic equations , 1998 .

[13]  R. Sani,et al.  Incompressible Flow and the Finite Element Method, Volume 1, Advection-Diffusion and Isothermal Laminar Flow , 1998 .

[14]  P. Colella,et al.  A Conservative Adaptive Projection Method for the Variable Density Incompressible Navier-Stokes Equations , 1998 .

[15]  S. Turek.  Efficient solvers for incompressible flow problems: An algorithmic approach . . , 1998 .

[16]  Stefan Turek,et al.  Efficient Solvers for Incompressible Flow Problems - An Algorithmic and Computational Approach , 1999, Lecture Notes in Computational Science and Engineering.

[17]  B. Bennett,et al.  Local Rectangular Refinement with Application to Nonreacting and Reacting Fluid Flow Problems , 1999 .

[18]  M S Day,et al.  Numerical simulation of laminar reacting flows with complex chemistry , 2000 .

[19]  J. Szmelter.  Incompressible flow and the finite element method , 2001 .

[20]  A. Schmidt,et al.  A Multi-mesh Finite Element Method for 3D Phase Field Simulations , 2003 .

[21]  Albert Cohen,et al.  Fully adaptive multiresolution finite volume schemes for conservation laws , 2003, Math. Comput..

[22]  Kai Schneider,et al.  An adaptive multiresolution method for combustion problems: application to flame ball–vortex interaction , 2005 .

[23]  Robert Eymard,et al.  Numerical Results Using a Colocated Finite-Volume Scheme on Unstructured Grids for Incompressible Fluid Flows , 2006 .

[24]  R. Eymard,et al.  Discretisation of heterogeneous and anisotropic diffusion problems on general non-conforming meshes. SUSHI: a scheme using stabilisation and hybrid interfaces , 2008, 0801.1430.

[25]  Raphaèle Herbin,et al.  A collocated finite volume scheme to solve free convection for general non-conforming grids , 2009, J. Comput. Phys..

[26]  Cosmin Safta,et al.  A high-order low-Mach number AMR construction for chemically reacting flows , 2010, J. Comput. Phys..

[27]  E. Hairer,et al.  Solving Ordinary Differential Equations II , 2010 .

[28]  Marc Massot,et al.  Adaptive time splitting method for multi-scale evolutionary partial differential equations , 2011, 1104.3697.

[29]  Christian Tenaud,et al.  TUTORIALS ON ADAPTIVE MULTIRESOLUTION FOR MESH REFINEMENT APPLIED TO FLUID DYNAMICS AND REACTIVE MEDIA PROBLEMS. , 2011 .

[30]  Max Duarte,et al.  Adaptive numerical methods in time and space for the simulation of multi-scale reaction fronts. (Méthodes numériques adaptatives pour la simulation de la dynamique de fronts de réaction multi-échelles en temps et en espace) , 2011 .

[31]  Benjamin Sanderse,et al.  Energy-conserving Runge-Kutta methods for the incompressible Navier-Stokes equations , 2013, J. Comput. Phys..

[32]  Carlos Pantano,et al.  A collocated method for the incompressible Navier-Stokes equations inspired by the Box scheme , 2013, J. Comput. Phys..

[33]  Marc Massot,et al.  Time–space adaptive numerical methods for the simulation of combustion fronts , 2013 .

[34]  Frédéric Gibou,et al.  A stable projection method for the incompressible Navier-Stokes equations on arbitrary geometries and adaptive Quad/Octrees , 2015, J. Comput. Phys..

[35]  M. Massot,et al.  A high-order Runge-Kutta method coupled to a multiresolution strategy to solve the incompressible Navier-Stokes equations , 2018 .

[36]  Barry F. Smith,et al.  PETSc Users Manual , 2019 .

[37]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[38]  Marie Postel,et al.  Approximations multiéchelles , 2022 .