Philippe Chatelain

R-leaping: accelerating the stochastic simulation algorithm by reaction leaps.

A novel algorithm is proposed for the acceleration of the exact stochastic simulation algorithm by a predefined number of reaction firings (R-leaping) that may occur across several reaction channels. In the present approach, the numbers of reaction firings are correlated binomial distributions and the sampling procedure is independent of any permutation of the reaction channels. This enables the algorithm to efficiently handle large systems with disparate rates, providing substantial computational savings in certain cases. Several mechanisms for controlling the accuracy and the appearance of negative species are described. The advantages and drawbacks of R-leaping are assessed by simulations on a number of benchmark problems and the results are discussed in comparison with established methods.

An immersed boundary-lattice-Boltzmann method for the simulation of the flow past an impulsively started cylinder

We present a lattice-Boltzmann method coupled with an immersed boundary technique for the simulation of bluff body flows. The lattice-Boltzmann method for the modeling of the Navier-Stokes equations, is enhanced by a forcing term to account for the no-slip boundary condition on a non-grid conforming boundary. We investigate two alternatives of coupling the boundary forcing term with the grid nodes, namely the direct and the interpolated forcing techniques. The present LB-IB methods are validated in simulations of the incompressible flow past an impulsively started cylinder at low and moderate Reynolds numbers. We present diagnostics such as the near wall vorticity field and the drag coefficient and comparisons with previous computational and experimental works and assess the advantages and drawbacks of the two techniques.

Short Note: A Fourier-based elliptic solver for vortical flows with periodic and unbounded directions

We present a computationally efficient, adaptive solver for the solution of the Poisson and Helmholtz equation used in flow simulations in domains with combinations of unbounded and periodic directions. The method relies on using FFTs on an extended domain and it is based on the method proposed by Hockney and Eastwood for plasma simulations. The method is well-suited to problems with dynamically growing domains and in particular flow simulations using vortex particle methods. The efficiency of the method is demonstrated in simulations of trailing vortices.

Evolutionary optimization of an anisotropic compliant surface for turbulent friction drag reduction

Direct numerical simulation (DNS) of the channel flow with an anisotropic compliant surface is performed in order to investigate its drag reduction effect in a fully developed turbulent flow. The computational domain is set to be 3δ×2δ×3δ, where δ is the channel half-width. The surface is passively driven by the pressure and wall-shear stress fluctuations, and the surface velocity provides a boundary condition for the fluid velocity field. An evolutionary optimization method (CMA-ES) is used to optimize the parameters of the anisotropic compliant surface. The optimization identifies several sets of parameters that result in a reduction of the friction drag with a maximum reduction rate of 8%. The primary mechanism for drag reduction is attributed to the decrease of the Reynolds shear stress (RSS) near the wall induced by the kinematics of the surface. The resultant wall motion is a uniform wave traveling downstream. The compliant wall, with the parameters found in the optimization study, is also tested in a computational domain that is doubled in the streamwise direction. The drag, however, is found to increase in the larger computational domain due to excessively large wall-normal velocity fluctuations.

Adaptive mesh refinement for stochastic reaction-diffusion processes

We present an algorithm for adaptive mesh refinement applied to mesoscopic stochastic simulations of spatially evolving reaction-diffusion processes. The transition rates for the diffusion process are derived on adaptive, locally refined structured meshes. Convergence of the diffusion process is presented and the fluctuations of the stochastic process are verified. Furthermore, a refinement criterion is proposed for the evolution of the adaptive mesh. The method is validated in simulations of reaction-diffusion processes as described by the Fisher-Kolmogorov and Gray-Scott equations.

A numerical study of the stabilitiy of helical vortices using vortex methods

We present large-scale parallel direct numerical simulations using particle vortex methods of the instability of the helical vortices. We study the instability of a single helical vortex and find good agreement with inviscid theory. We outline equilibrium configurations for three double helical vortices—similar to those produced by three blade wind turbines. The simulations confirm the stability of the inviscid model, but predict a breakdown of the vortical system due to viscosity.

D-leaping: Accelerating stochastic simulation algorithms for reactions with delays

We propose a novel, accelerated algorithm for the approximate stochastic simulation of biochemical systems with delays. The present work extends existing accelerated algorithms by distributing, in a time adaptive fashion, the delayed reactions so as to minimize the computational effort while preserving their accuracy. The accuracy of the present algorithm is assessed by comparing its results to those of the corresponding delay differential equations for a representative biochemical system. In addition, the fluctuations produced from the present algorithm are comparable to those from an exact stochastic simulation with delays. The algorithm is used to simulate biochemical systems that model oscillatory gene expression. The results indicate that the present algorithm is competitive with existing works for several benchmark problems while it is orders of magnitude faster for certain systems of biochemical reactions.

Large Scale Three-Dimensional Boundary Element Simulation of Subduction

We present a novel approach for modeling subduction using a Multipole-accelerated Boundary Element Method (BEM). The present approach allows large-scale modeling with a reduced number of elements and scales linearly with the problem size. For the first time the BEM has been applied to a subduction model in a spherical planet with an upper-lower mantle discontinuity, in conjunction with a free-surface mesh algorithm.

Particle Mesh Hydrodynamics for Astrophysics Simulations

We present a particle method for the simulation of three dimensional compressible hydrodynamics based on a hybrid Particle-Mesh discretization of the governing equations. The method is rooted on the regularization of particle locations as in remeshed Smoothed Particle Hydrodynamics (rSPH). The rSPH method was recently introduced to remedy problems associated with the distortion of computational elements in SPH, by periodically re-initializing the particle positions and by using high order interpolation kernels. In the PMH formulation, the particles solely handle the convective part of the compressible Euler equations. The particle quantities are then interpolated onto a mesh, where the pressure terms are computed. PMH, like SPH, is free of the convection CFL condition while at the same time it is more efficient as derivatives are computed on a mesh rather than particle-particle interactions. PMH does not detract from the adaptive character of SPH and allows for control of its accuracy. We present simulations of a benchmark astrophysics problem demonstrating the capabilities of this approach.

A software framework for the portable parallelization of particle-mesh simulations

We present a software framework for the transparent and portable parallelization of simulations using particle-mesh methods. Particles are used to transport physical properties and a mesh is required in order to reinitialize the distorted particle locations, ensuring the convergence of the method. Field quantities are computed on the particles using fast multipole methods or by discretizing and solving the governing equations on the mesh. This combination of meshes and particles presents a challenging set of parallelization issues. The present library addresses these issues for a wide range of applications, and it enables orders of magnitude increase in the number of computational elements employed in particle methods. We demonstrate the performance and scalability of the library on several problems, including the first-ever billion particle simulation of diffusion in real biological cell geometries.