Orestis Malaspinas

Estimating Allele Age and Selection Coefficient from Time-Serial Data

Recent advances in sequencing technologies have made available an ever-increasing amount of ancient genomic data. In particular, it is now possible to target specific single nucleotide polymorphisms in several samples at different time points. Such time-series data are also available in the context of experimental or viral evolution. Time-series data should allow for a more precise inference of population genetic parameters and to test hypotheses about the recent action of natural selection. In this manuscript, we develop a likelihood method to jointly estimate the selection coefficient and the age of an allele from time-serial data. Our method can be used for allele frequencies sampled from a single diallelic locus. The transition probabilities are calculated by approximating the standard diffusion equation of the Wright–Fisher model with a one-step process. We show that our method produces unbiased estimates. The accuracy of the method is tested via simulations. Finally, the utility of the method is illustrated with an application to several loci encoding coat color in horses, a pattern that has previously been linked with domestication. Importantly, given our ability to estimate the age of the allele, it is possible to gain traction on the important problem of distinguishing selection on new mutations from selection on standing variation. In this coat color example for instance, we estimate the age of this allele, which is found to predate domestication.

Synchrotron X-ray microtomography and lattice Boltzmann simulations of gas flow through volcanic pumices

To illustrate the advances made in permeability calculations combining X-ray microtomography and lattice Boltzmann method simulations, a sample suite of different types of pumices was investigated. Large three-dimensional images at high spatial resolution were collected at three different synchrotron facilities (Elettra, SLS, and ESRF). Single phase gas flow simulations were done on computer clusters with a highly parallelized lattice Boltzmann code, named Palabos. Permeability measurements obtained by gas flow simulation were compared to lab measurements of pumices produced by the Kos Plateau Tuff eruption to validate the method. New permeability data for pumices from other silicic volcanic deposits is presented, and an empirical model for permeability is tested using geometrical and topological data, i.e., tortuosity, specific surface area, and total and connected porosity.

Advances in multi-domain lattice Boltzmann grid refinement

Grid refinement has been addressed by different authors in the lattice Boltzmann method community. The information communication and reconstruction on grid transitions is of crucial importance from the accuracy and numerical stability point of view. While a decimation is performed when going from the fine to the coarse grid, a reconstruction must performed to pass form the coarse to the fine grid. In this context, we introduce a decimation technique for the copy from the fine to the coarse grid based on a filtering operation. We show this operation to be extremely important, because a simple copy of the information is not sufficient to guarantee the stability of the numerical scheme at high Reynolds numbers. Then we demonstrate that to reconstruct the information, a local cubic interpolation scheme is mandatory in order to get a precision compatible with the order of accuracy of the lattice Boltzmann method. These two fundamental extra-steps are validated on two classical 2D benchmarks, the 2D circular cylinder and the 2D dipole-wall collision. The latter is especially challenging from the numerical point of view since we allow strong gradients to cross the refinement interfaces at a relatively high Reynolds number of 5000. A very good agreement is found between the single grid and the refined grid cases. The proposed grid refinement strategy has been implemented in the parallel open-source library Palabos.

Parallel performance of an IB-LBM suspension simulation framework

We present performance results from ficsion, a general purpose parallel suspension solver, employing the Immersed-Boundary lattice-Boltzmann method (IB-LBM). ficsion is built on top of the open-source LBM framework Palabos, making use of its data structures and their inherent parallelism. We describe in brief the implementation and present weak and strong scaling results for simulations of dense red blood cell suspensions. Despite its complexity the simulations demonstrate a fairly good, close to linear scaling, both in the weak and strong scaling scenarios.

Simulation of generalized Newtonian fluids with the lattice Boltzmann method

This paper proposes a study of the computational efficiency of a lattice Boltzmann model (LBM) solver to simulate the behavior of a generalized Newtonian fluid. We present recent progress concerning a 4-1 planar contraction considering a power-law and a Carreau-law model. First we compare the power-law model for a Poiseuille flow with the analytical solution, and show that our model is second-order accurate in space. Then we compare the results obtained with LBM for both laws to those obtained using a commercial finite element solver for the 4-1 plane sharp corner contraction.

A spatio-temporal model for spontaneous thrombus formation in cerebral aneurysms.

We propose a new numerical model to describe thrombus formation in cerebral aneurysms. This model combines CFD simulations with a set of bio-mechanical processes identified as being the most important to describe the phenomena at a large space and time scales. The hypotheses of the model are based on in vitro experiments and clinical observations. We document that we can reproduce very well the shape and volume of patient specific thrombus segmented in giant aneurysms.

Generalized three-dimensional lattice Boltzmann color-gradient method for immiscible two-phase pore-scale imbibition and drainage in porous media

This article presents a three-dimensional numerical framework for the simulation of fluid-fluid immiscible compounds in complex geometries, based on the multiple-relaxation-time lattice Boltzmann method to model the fluid dynamics and the color-gradient approach to model multicomponent flow interaction. New lattice weights for the lattices D3Q15, D3Q19, and D3Q27 that improve the Galilean invariance of the color-gradient model as well as for modeling the interfacial tension are derived and provided in the Appendix. The presented method proposes in particular an approach to model the interaction between the fluid compound and the solid, and to maintain a precise contact angle between the two-component interface and the wall. Contrarily to previous approaches proposed in the literature, this method yields accurate solutions even in complex geometries and does not suffer from numerical artifacts like nonphysical mass transfer along the solid wall, which is crucial for modeling imbibition-type problems. The article also proposes an approach to model inflow and outflow boundaries with the color-gradient method by generalizing the regularized boundary conditions. The numerical framework is first validated for three-dimensional (3D) stationary state (Jurins law) and time-dependent (Washburns law and capillary waves) problems. Then, the usefulness of the method for practical problems of pore-scale flow imbibition and drainage in porous media is demonstrated. Through the simulation of nonwetting displacement in two-dimensional random porous media networks, we show that the model properly reproduces three main invasion regimes (stable displacement, capillary fingering, and viscous fingering) as well as the saturating zone transition between these regimes. Finally, the ability to simulate immiscible two-component flow imbibition and drainage is validated, with excellent results, by numerical simulations in a Berea sandstone, a frequently used benchmark case used in this field, using a complex geometry that originates from a 3D scan of a porous sandstone. The methods presented in this article were implemented in the open-source PALABOS library, a general C++ matrix-based library well adapted for massive fluid flow parallel computation.

Advanced large-eddy simulation for lattice Boltzmann methods: The approximate deconvolution model

The aim of this paper is to extend the approximate deconvolutionmodel for large-eddy simulations to the lattice Boltzmann method. This approach allows to directly act on the velocity distribution function and is based on the intrinsic nonlinearities of the lattice Boltzmann methods. It is not a straightforward extrapolation of classical eddy-viscosity models developed within the Navier–Stokes framework, which exhibits a convective quadratic nonlinearity in the incompressible flow case. A simple implementation is presented, which relies on the implementation of an ad hoc linear filter in any basic lattice Boltzmann solver. The new model is validated on the turbulent, time developing mixing layer, and a very satisfactory agreement is found with existing direct numerical simulations results. The equivalent Navier-Stokes-type macroscopic model is also discussed.

Sensitivity analysis and determination of free relaxation parameters for the weakly-compressible MRT-LBM schemes

Lattice Boltzmann methods (LBMs) are very efficient for computational fluid dynamics, and for capturing the dynamics of weak acoustic fluctuations. It is known that multi-relaxation-time lattice Boltzmann method (MRT-LBM) appears as a very robust scheme with high precision. There exist several free relaxation parameters in the MRT-LBM. Although these parameters have been tuned via linear analysis, the sensitivity analysis of these parameters and other related parameters is still not sufficient for describing the behavior of the dispersion and dissipation relations of the MRT-LBM. Previous researches have shown that the bulk dissipation in the MRT-LBM induces a significant over-damping of acoustic disturbances. This indicates that the classical MRT-LBM is not best suited to recover the correct behavior of pressure fluctuations. In wave-number space, the first/second-order sensitivity analyses of matrix eigenvalues are used to address the sensitivity of the wavenumber magnitudes to the dispersion-dissipation relations. By the first-order sensitivity analysis, the numerical behaviors of the group velocity of the MRT-LBM are first obtained. Afterwards, the distribution sensitivities of the matrix eigenvalues corresponding to the linearized form of the MRT-LBM are investigated in the complex plane. Based on the sensitivity analysis and an effective algorithm of recovering linearized Navier-Stokes equations (L-NSEs) from linearized MRT-LBM (L-MRT-LBM), we propose some simplified optimization strategies to determine the free relaxation parameters of the MRT-LBM. Meanwhile, the dispersion and dissipation relations of the optimal MRT-LBM are quantitatively compared with the exact dispersion and dissipation relations. At last, some numerical validations on classical acoustic benchmark problems are shown to assess the new optimal MRT-LBM.

Noise source identification with the lattice Boltzmann method

In this paper the sound source identification problem is addressed with the use of the lattice Boltzmann method. To this aim, a time-reversed problem coupled to a complex differentiation method is used. In order to circumvent the inherent instability of the time-reversed lattice Boltzmann scheme, a method based on a split of the lattice Boltzmann equation into a mean and a perturbation component is used. Lattice Boltzmann method formulation around an arbitrary base flow is recalled and specific applications to acoustics are presented. The implementation of the noise source detection method for two-dimensional weakly compressible (low Mach number) flows is discussed, and the applicability of the method is demonstrated.