Article history: Received 30 July 2015 Received in revised form 11 December 2015 Accepted 11 April 2016 Available online 14 April 2016

Article history: Received 7 April 2016 Received in revised form 26 October 2016 Accepted 12 November 2016 Available online 24 November 2016

We investigate discrete kinetic models in the Fluid dynamic limit described by the Euler system and the Navier-Stokes correction obtained by the Chapman Enskog procedure. We show why reliable “small” systems can be expected only for small Mach numbers and derive a calculus for designing models for given Prandtl numbers.

A . This report analyzes the long time stability of four methods for non-iterative, sub-physics, uncoupling for the evolutionary Stokes-Darcy problem. The four methods uncouple each time step into separate Stokes and Darcy solves using ideas from splitting methods. Three methods uncouple sequentially while one is a parallel uncoupling method. We prove long time stability of four splitting based...

∧ for determining the singular force for the boundary of a rigid objectwith prescribedmotion in 2D [Sheng Xu, The immersed interface method for simulating prescribed motion of rigid objects in an incompressible viscous flow, J. Comput. Phys. 227 (2008) 5045–5071]. ∧ Necessary formulas for extending the approach to 3D ∧ are derived in this ∧ work. With the implementation of these formulas, the i...

We study the incompressible Navier-Stokes equations with a fractional Laplacian and prove the existence of discontinuous LerayHopf solutions in the largest critical space with arbitrarily small initial data.

We estimate the asymptotic behavior for the Stokes solutions, with external forces first. We ∧ found that if there ∧ are external forces, then the energy decays ∧ slowly even if the forces ∧ decay quickly. Then, we also obtain the asymptotic ∧ behavior in the temporal-spatial direction for weak solutions of the Navier–Stokes equations. We also provide a simple example of external forces which s...

Juan Du, I.M. Navon2,∗,†, J.L. Steward, A.K. Alekseev, Zhendong Luo 1 School of Science, Beijing Jiaotong University, Beijing 100044, China. 2 Department of Scientific Computing, Florida State University, Tallahassee, FL 32306-4120, USA. 3 Moscow Institute of Physics and Technology, Moscow 141700, Russia. 4 School of Mathematics and Physics, North China Electric Power University, Beijing 102206...