A Parareal in Time Semi-implicit Approximation of the Navier-Stokes Equations

By Paul F. Fischer, Frédéric Hecht, Yvon Maday. 2005

132 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis, Statistical and Nonlinear Physics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Beth A. Wingate
2. Terry S. Haut
3. G. Em Karniadakis
4. Zhen Li
5. Ansel L. Blumers
6. Tony Lelièvre
7. Gabriel Turinici
8. Frédéric Legoll

In Numerical Analysis

1. Beth A. Wingate
2. Terry S. Haut
3. G. Em Karniadakis
4. Zhen Li
5. Ansel L. Blumers
6. Tony Lelièvre
7. Giovanni Samaey
8. Frédéric Legoll

In Statistical and Nonlinear Physics

1. Zhen Li
2. Tony Lelièvre
3. Giovanni Samaey
4. Frédéric Legoll
5. Gabriel Turinici
6. Beth A. Wingate
7. Terry S. Haut
8. G. Em Karniadakis

Citations in the corpus

• A Micro-Macro Parareal Algorithm: Application to Singularly Perturbed Ordinary Differential Equations (2012, methodology): “Since its introduction in [26], the parareal strategy has been applied to a wide range of problems, including fluid-structure interaction [11], Navier–Stokes equation simulation [12], reservoir simulation [15], etc.”
• An Asymptotic Parallel-in-Time Method for Highly Oscillatory PDEs (2013, methodology): “Early applications of the parareal method include simulations of molecular dynamics [4], the Navier Stokes equation [15], and quantum control problems [26]; additional references can be found in [34].”
• The Parareal in Time Iterative Solver: a Further Direction to Parallel Implementation (2005, methodology): “[2001], with a coarser discretization in space ∆X (see also Fischer et al. [2003]) or even, a simpler physical model, as was implemented in Maday and Turinici [2003].”
• Supervised parallel-in-time algorithm for long-time Lagrangian simulations of stochastic dynamics: Application to hydrodynamics (2019, methodology): “The traditional Parareal scheme has been applied to a wide range of problems, including fluid-structure interactions [16], reservoir simulation [17], approximation to Navier-Stokes equations [18], turbulent plasma flow [19], and even to fractional partial differential equations [20].”
• Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model (2014, methodology): “In this paper the coarse solver is only based on a coarse time step, we refer to [22] for a consideration of a coarse time and space based solver with application to Navier–Stokes problem.”