A modified fractional step method for fluid–structure interaction problems

We propose a Lagrangian fluid formulation particularly suitable for fluid–structure interaction (FSI) simulation involving free-surface flows and light-weight structures. The technique combines the features of fractional step and quasi-incompressible approaches. The fractional momentum equation is modified so as to include an approximation for the current-step pressure using the assumption of quasi-incompressibility. The volumetric term in the tangent matrix is approximated allowing for the element-wise pressure condensation in the prediction step. The modified fractional momentum equation can be readily coupled with a structural code in a partitioned or monolithic fashion. The use of the quasi-incompressible prediction ensures convergent fluid–structure solution even for challenging cases when the densities of the fluid and the structure are similar. Once the prediction was obtained, the pressure Poisson equation and momentum correction equation are solved leading to a truly incompressible solution in the fluid domain except for the boundary where essential pressure boundary condition is prescribed. The paper concludes with two benchmark cases, highlighting the advantages of the method and comparing it with similar approaches proposed formerly.Peer Reviewe

A semi-explicit multi-step method for solving incompressible navier-stokes equations

The fractional step method is a technique that results in a computationally-efficient implementation of Navier–Stokes solvers. In the finite element-based models, it is often applied in conjunction with implicit time integration schemes. On the other hand, in the framework of finite difference and finite volume methods, the fractional step method had been successfully applied to obtain predictor-corrector semi-explicit methods. In the present work, we derive a scheme based on using the fractional step technique in conjunction with explicit multi-step time integration within the framework of Galerkin-type stabilized finite element methods. We show that under certain assumptions, a Runge–Kutta scheme equipped with the fractional step leads to an efficient semi-explicit method, where the pressure Poisson equation is solved only once per time step. Thus, the computational cost of the implicit step of the scheme is minimized. The numerical example solved validates the resulting scheme and provides the insights regarding its accuracy and computational efficiency.Peer ReviewedPostprint (published version

A semi-explicit multi-step method for solving incompressible navier-stokes equations

The fractional step method is a technique that results in a computationally-efficient implementation of Navier–Stokes solvers. In the finite element-based models, it is often applied in conjunction with implicit time integration schemes. On the other hand, in the framework of finite difference and finite volume methods, the fractional step method had been successfully applied to obtain predictor-corrector semi-explicit methods. In the present work, we derive a scheme based on using the fractional step technique in conjunction with explicit multi-step time integration within the framework of Galerkin-type stabilized finite element methods. We show that under certain assumptions, a Runge–Kutta scheme equipped with the fractional step leads to an efficient semi-explicit method, where the pressure Poisson equation is solved only once per time step. Thus, the computational cost of the implicit step of the scheme is minimized. The numerical example solved validates the resulting scheme and provides the insights regarding its accuracy and computational efficienc

An explicit/implicit Runge–Kutta-based PFEM model for the simulation of thermally coupled incompressible flows

A semi-explicit Lagrangian scheme for the simulation of thermally coupled incompressible flow problems is presented. The model relies on combining an explicit multi-step solver for the momentum equation with an implicit heat equation solver. Computational cost of the model is reduced via application of an efficient strategy adopted for the solution of momentum/continuity system by the authors in their previous work. The applicability of the method to solving thermo-mechanical problems is studied via various numerical examples

An embedded approach for immiscible multi-fluid problems

An embedded formulation for the simulation of immiscible multi-fluid problems is proposed. The method is particularly designed for handling gas-liquid systems. Gas and liquid are modeled using the Eulerian and the Lagrangian formulation, respectively. The Lagrangian domain (liquid) moves on top of the fixed Eulerian mesh. The location of the material interface is exactly defined by the position of the boundary mesh of the Lagrangian domain. The individual fluid problems are solved in a partitioned fashion and are coupled using a Dirichlet-Neumann algorithm. Representation of the pressure discontinuity across the interface does not require any additional techniques being an intrinsic feature of the method. The proposed formulation is validated, and its potential applications are shown

An explicit/implicit Runge–Kutta-based PFEM model for the simulation of thermally coupled incompressible flows

The final publication is available at Springer via http://dx.doi.org/10.1007/s40571-019-00229-0A semi-explicit Lagrangian scheme for the simulation of thermally coupled incompressible flow problems is presented. The model relies on combining an explicit multi-step solver for the momentum equation with an implicit heat equation solver. Computational cost of the model is reduced via application of an efficient strategy adopted for the solution of momentum/continuity system by the authors in their previous work. The applicability of the method to solving thermo-mechanical problems is studied via various numerical examples.Peer ReviewedPostprint (author's final draft

A monolithic FE formulation for the analysis of membranes in fluids

We propose here an efficient approach for treating the interaction between membranes and fluids. Slight compressibility of the fluid is assumed. Classical total Lagrangian formulation including wrinkling is adopted for the membrane representation, whereas fluid is treated in an updated Lagrangian manner, developed in the current work. Assumption of slight compressibility of the fluid enables one to define the monolithic fluid-membrane system in a natural way. The displacements are the primary variables of both the fluid and the membrane domains. The formulation adopts the Particle Finite Element Method (PFEM) philosophy for free-surface identification and mesh regeneration. Three examples illustrate the functionality of the formulation in application to FSI problems involving motion of membranes in wate

An enhanced non-oscillatory BFECC algorithm for finite element solution of advective transport problems

In this paper, the so-called “back and forth error compensation correction (BFECC)” methodology is utilized to improve the solvers developed for the advection equation. Strict obedience to the so-called “discrete maximum principle” is enforced by incorporating a gradient–based limiter into the BFECC algorithm. The accuracy of the BFECC algorithm in capturing the steep–fronts in hyperbolic scalar–transport problems is improved by introducing a controlled anti–di¿usivity. This is achieved at the cost of performing an additional backward sub–solution–step and modifying the formulation of the error compensation accordingly. The performance of the proposed methodology is assessed by solving a series of benchmarks utilizing di¿erent combinations of the BFECC algorithms and the underlying numerical schemes. Results are presented for both the structured and unstructured meshes.This work was performed within the framework of AMADEUS project (”Advanced Multi-scAle moDEling of coupled mass transport for improving water management in fUel cellS”, reference number PGC2018-101655-B-I00) supported by the Ministerio de Ciencia, Innovacion e Universidades of Spain. The authors also acknowledge financial support of the mentioned Ministry via the “Severo Ochoa Programme” for Centres of Excellence in R&D (referece: CEX2018-000797-S) given to the International Centre for Numerical Methods in Engineering (CIMNE).Peer ReviewedPostprint (published version

A Unified arbitrary lagrangian-eulerian model for fluid-structure interaction problems involving flows in flexible channels

In this work a finite element-based model for analyzing incompressible flows in flexible channels is presented. The model treats the fluid-solid interaction problem in a monolithic way, where the governing equations for both sub-domains are solved on a single moving grid taking advantage of an arbitrary Lagrangian/Eulerian framework (ALE). The unified implementation of the governing equations for both sub-domains is developed, where these are distinguished only in terms of the mesh-moving strategy and the constitutive equation coefficients. The unified formulation is derived considering a Newtonian incompressible fluid and a hypoelastic solid. Hypoelastic constitutive law is based on the strain rate and thus naturally facilitates employing velocity as a kinematic variable in the solid. Unifying the form of the governing equations and defining a semi-Lagrangian interface mesh-motion algorithm , one obtains the coupled problem formulated in terms of a unique kinematic variable. Resulting monolithic system is characterized by reduced variable heterogeneity resembling that of a single-media problem. The model used in conjunction with algebraic multigrid linear solver exhibits attractive convergence rates. The model is tested using a 2D and a 3D example.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. The authors acknowledge financial support from the Ministerio de Ciencia, Innovacion e Universidades of Spain via the “Severo Ochoa” Programme for Centres of Excellence in R&D (Referece: CEX2018-000797-S) as well as via AMADEUS Project Grant (Reference: PGC2018-101655-B-I00).Peer ReviewedPostprint (published version

Toward droplet dynamics simulation in polymer electrolyte membrane fuel cells: three-dimensional numerical modeling of confined water droplets with dynamic contact angle and hysteresis

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Mohammad R. Hashemi, Pavel B. Ryzhakov, and Riccardo Rossi, "Toward droplet dynamics simulation in polymer electrolyte membrane fuel cells: Three-dimensional numerical modeling of confined water droplets with dynamic contact angle and hysteresis", Physics of Fluids 33, 122109 (2021) and may be found at https://doi.org/10.1063/5.0073331This work focuses on three-dimensional simulation of the dynamics of droplets with contact–angle hysteresis. In order to consistently model the dynamics of the contact– line, a combination of the linear molecular kinetic theory and the hydrodynamic theory is implemented in the present numerical method. Without presetting the contact–line and/or the contact–angle, such simulations are generally prone to irregularities at the contact–line, which are mainly due to the imposition of the pinning and unpinning mechanisms associated with the hysteresis phenomenon. An effective treatment for this issue is proposed based on a simple procedure for calculating the nodal contact–angle within the framework of enriched finite element/level set method. The resulting method also benefits from a manipulated momentum conservation equation that incorporates the effect of the liquid mass conservation correction, which is essentially important for simulations with a rather long (physical) run–time. In this paper, the proposed numerical model is validated against the previously published experimental data addressing the configuration of a water droplet on a tilted rough hydrophobic surface. In this test, the effect of the contact–line pinning as the underlying mechanism for droplet hysteresis phenomenon is also studied. The model is further employed to simulate a liquid droplet confined in a channel in the presence of air flow.This work was performed within the framework of AMADEUS project (“Advanced Multi-scAle moDEling of coupled mass transport for improving water management in fUel cellS,” Reference Number PGC2018–101655-B-I00) supported by the Ministerio de Ciencia, Innovacion e Universidades of Spain. The authors acknowledge the financial support of the mentioned Ministry via the “Severo Ochoa Programme” for Centres of Excellence in R&D (Reference No. CEX2018–000797-S) given to the International Centre for Numerical Methods in Engineering (CIMNE). The authors also acknowledge PRACE for awarding us access to MareNostrum hosted by Barcelona Supercomputing Center, Spain (Project Reference No. 2010PA5560).Peer ReviewedPostprint (author's final draft