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The lattice Boltzmann method (LBM) is known to suffer from stability issues when the collision model relies on the BGK approximation, especially in the zero viscosity limit and for non-vanishing Mach numbers. To tackle this problem, two kinds of solutions were proposed in the literature. They consist in changing either the numerical discretization (finite-volume, finite-difference, spectral-element, etc.) of the discrete velocity Boltzmann equation (DVBE), or the collision model. In this work, the latter solution is investigated in detail. More precisely, we propose a comprehensive comparison of (static relaxation time based) collision models, in terms of stability, and with preliminary results on their accuracy, for the simulation of isothermal high-Reynolds number flows in the (weakly) compressible regime. It starts by investigating the possible impact of collision models on the macroscopic behaviour of stream-and-collide based D2Q9-LBMs, which clarifies the exact physical properties of collision models on LBMs. It is followed by extensive linear and numerical stability analyses, supplemented with an accuracy study based on the transport of vortical structures over long distances. In order to draw conclusions as generally as possible, the most common moment spaces (raw, central, Hermite, central Hermite and cumulant), as well as regularized approaches, are considered for the comparative studies. LBMs based on dynamic collision mechanisms (entropic collision, subgrid-scale models, explicit filtering, etc.) are also briefly discussed. This article is part of the theme issue ‘Fluid dynamics, soft matter and complex systems: recent results and new methods’.

Reactive processes associated with multiphase flows play a significant role in mass transport in unsaturated porous media. For example, the effect of reactions on the solid matrix can affect the formation and stability of fingering instabilities associated with the invasion of a buoyant non-wetting fluid. In this study, we focus on the formation and stability of capillary channels of a buoyant non-wetting fluid (developed because of capillary instabilities) and their impact on the transport and distribution of a reactant in the porous medium. We use a combination of pore-scale numerical calculations based on a multiphase reactive lattice Boltzmann model (LBM) and scaling laws to quantify (i) the effect of dissolution on the preservation of capillary instabilities, (ii) the penetration depth of reaction beyond the dissolution/melting front, and (iii) the temporal and spatial distribution of dissolution/melting under different conditions (concentration of reactant in the non-wetting fluid, injection rate). Our results show that, even for tortuous non-wetting fluid channels, simple scaling laws assuming an axisymmetrical annular flow can explain (i) the exponential decay of reactant along capillary channels, (ii) the dependence of the penetration depth of reactant on a local Péclet number (using the non-wetting fluid velocity in the channel) and more qualitatively (iii) the importance of the melting/reaction efficiency on the stability of non-wetting fluid channels. Our numerical method allows us to study the feedbacks between the immiscible multiphase fluid flow and a dynamically evolving porous matrix (dissolution or melting) which is an essential component of reactive transport in porous media.

We review a methodology to design, implement and execute multi-scale and multi-science numerical simulations. We identify important ingredients of multi-scale modelling and give a precise definition of them. Our framework assumes that a multi-scale model can be formulated in terms of a collection of coupled single-scale submodels. With concepts such as the scale separation map, the generic submodel execution loop (SEL) and the coupling templates, one can define a multi-scale modelling language which is a bridge between the application design and the computer implementation. Our approach has been successfully applied to an increasing number of applications from different fields of science and technology.

The inherent complexity of biomedical systems is well recognized; they are multiscale, multiscience systems, bridging a wide range of temporal and spatial scales. While the importance of multiscale modelling in this context is increasingly recognized, there is little underpinning literature on the methodology and generic description of the process. The COAST (complex autonoma simulation technique) project aims to address this by developing a multiscale, multiscience framework, coined complex autonoma (CxA), based on a hierarchical aggregation of coupled cellular automata (CA) and agent-based models (ABMs). The key tenet of COAST is that a multiscale system can be decomposed into N single-scale CA or ABMs that mutually interact across the scales. Decomposition is facilitated by building a scale separation map on which each single-scale system is represented according to its spatial and temporal characteristics. Processes having well-separated scales are thus easily identified as the components of the multiscale model. This paper focuses on methodology, introduces the concept of the CxA and demonstrates its use in the generation of a multiscale model of the physical and biological processes implicated in a challenging and clinically relevant problem, namely coronary artery in-stent restenosis.

Multiscale simulations model phenomena across natural scales using monolithic or component-based code, running on local or distributed resources. In this work, we investigate the performance of distributed multiscale computing of component-based models, guided by six multiscale applications with different characteristics and from several disciplines. Three modes of distributed multiscale computing are identified: supplementing local dependencies with large-scale resources, load distribution over multiple resources, and load balancing of small- and large-scale resources. We find that the first mode has the apparent benefit of increasing simulation speed, and the second mode can increase simulation speed if local resources are limited. Depending on resource reservation and model coupling topology, the third mode may result in a reduction of resource consumption.

In this paper we present the behaviours of a simple credit market model built upon a static directed complex network topology. We found that the market structure plays a key role on the stability of such a model. Cyclic topologies accumulate more debt than acyclic ones, and when the total cash is less than the total debt, the market becomes unstable and exhibits chaotic behaviour. Exogenous creation of currency is used to control the market stability. Two regimes of control emerge depending on the credit market structure. First, power law control is needed for acyclic random topologies built upon Erdos-Rényi and Barabasi-Albert algorithms. Second, exponential control is needed to stabilize cyclic market built with the Watts-Strogatz algorithm. Dans cet article, nous présentons les comportements d’un modèle simplifié du marché du crédit. La structure du marché est construite autour d’un réseau complexe statique. Nos résultats montrent que la structure du marché joue un rôle crucial dans la stabilité du modèle. Les topologies cycliques accumulent plus de dettes que les topologies acycliques et lorsque la dette accumulée excède le montant total des liquidités, le marché devient instable et converge vers un comportement chaotique. La création exogène de liquidité est utilisée pour contrôler la stabilité du marché. Deux types de contrôle qui dépendent de la structure du marché du crédit émergent. Le premier type de contrôle est le contrôle suivant une loi de puissance. Ce contrôle est nécessaire pour stabiliser un marché basé sur les topologies acycliques du type réseaux de Erdos-Rényi et Barabasi-Albert. Le second type de contrôle est le contrôle suivant une loi exponentielle qui est nécessaire pour stabiliser un marché basé sur les topologies cycliques du type réseaux de Watts-Strogatz.

The lattice Boltzmann method (LBM) is known to suffer from stability issues when the collision model relies on the BGK approximation, especially in the zero viscosity limit and for non-vanishing Mach numbers. To tackle this problem, two kinds of solutions were proposed in the literature. They consist in changing either the numerical discretization (finite-volume, finite-difference, spectral-element, etc.) of the discrete velocity Boltzmann equation (DVBE), or the collision model. In this work, the latter solution is investigated in detail. More precisely, we propose a comprehensive comparison of (static relaxation time based) collision models, in terms of stability, and with preliminary results on their accuracy, for the simulation of isothermal high-Reynolds number flows in the (weakly) compressible regime. It starts by investigating the possible impact of collision models on the macroscopic behaviour of stream-and-collide based D2Q9-LBMs, which clarifies the exact physical properties of collision models on LBMs. It is followed by extensive linear and numerical stability analyses, supplemented with an accuracy study based on the transport of vortical structures over long distances. In order to draw conclusions as generally as possible, the most common moment spaces (raw, central, Hermite, central Hermite and cumulant), as well as regularized approaches, are considered for the comparative studies. LBMs based on dynamic collision mechanisms (entropic collision, subgrid-scale models, explicit filtering, etc.) are also briefly discussed. This article is part of the theme issue ‘Fluid dynamics, soft matter and complex systems: recent results and new methods’.

We review a methodology to design, implement and execute multi-scale and multi-science numerical simulations. We identify important ingredients of multi-scale modelling and give a precise definition of them. Our framework assumes that a multi-scale model can be formulated in terms of a collection of coupled single-scale submodels. With concepts such as the scale separation map, the generic submodel execution loop (SEL) and the coupling templates, one can define a multi-scale modelling language which is a bridge between the application design and the computer implementation. Our approach has been successfully applied to an increasing number of applications from different fields of science and technology.