A low diffusive Lagrange-remap scheme for the simulation of violent air-water free-surface flows

36p. Submitted to Journal of Computational Physics.In 2002, Després and Lagoutiére proposed a low-diffusive advection scheme for pure transport equation problems, which is particularly accurate for step-shaped solutions, and thus suited for interface tracking procedure by a color function. This has been extended by Kokh and Lagoutiére in the context of compressible multifluid flows using a five-equation model. In this paper, we explore a simplified variant approach for gas-liquid three-equation models. The numerical scheme has two ingredients: a robust remapped Lagrange solver for the solution of the volume-averaged equations, and a low diffusive compressive scheme for the advection of the gas mass fraction. Numerical experiments show the performance of the computational approach on various flow reference problems: dam break, sloshing of a tank filled with water, water-water impact and finally a case of Rayleigh-Taylor instability. One of the advantage of the present interface capturing solver is its natural implementation on parallel processors or computers. In particular, we are confident on its implementation on Graphics Processing Units (GPU) with high speedups

Comparison of multiphase SPH and LBM approaches for the simulation of intermittent flows

Smoothed Particle Hydrodynamics (SPH) and Lattice Boltzmann Method (LBM) are increasingly popular and attractive methods that propose efficient multiphase formulations, each one with its own strengths and weaknesses. In this context, when it comes to study a given multi-fluid problem, it is helpful to rely on a quantitative comparison to decide which approach should be used and in which context. In particular, the simulation of intermittent two-phase flows in pipes such as slug flows is a complex problem involving moving and intersecting interfaces for which both SPH and LBM could be considered. It is a problem of interest in petroleum applications since the formation of slug flows that can occur in submarine pipelines connecting the wells to the production facility can cause undesired behaviors with hazardous consequences. In this work, we compare SPH and LBM multiphase formulations where surface tension effects are modeled respectively using the continuum surface force and the color gradient approaches on a collection of standard test cases, and on the simulation of intermittent flows in 2D. This paper aims to highlight the contributions and limitations of SPH and LBM when applied to these problems. First, we compare our implementations on static bubble problems with different density and viscosity ratios. Then, we focus on gravity driven simulations of slug flows in pipes for several Reynolds numbers. Finally, we conclude with simulations of slug flows with inlet/outlet boundary conditions. According to the results presented in this study, we confirm that the SPH approach is more robust and versatile whereas the LBM formulation is more accurate and faster

Reduced-order modeling of parametrized finite element solutions by the pod-isat technique. application to aircraft air control systems

A combined Proper Orthogonal Decomposition (POD) + In Situ Adaptive Tabulation (ISAT) is proposed for the representation of parameter-dependent solutions of coupled partial differential equations (PDE). The method is tested on a coupled fluidthermal problem: the design of a simplified aircraft air control system. Furthermore, the control of the method’s accuracy is discussed, leading to the metamodeling of the residual itself. The presented POD-ISAT approach provides by its flexibility and robustness an appropriate representation of the solutions for different use cases (sensitivity analysis, optimization, etc.

Guaranteed control of switched control systems using model order reduction and state-space bisection

This paper considers discrete-time linear systems controlled by a quantized law, i.e., a piecewise constant time function taking a finite set of values. We show how to generate the control by, first, applying model reduction to the original system, then using a "state-space bisection" method for synthesizing a control at the reduced-order level, and finally computing an upper bound to the deviations between the controlled output trajectories of the reduced-order model and those of the original model. The effectiveness of our approach is illustrated on several examples of the literature