[Paper Review] Comparison of multiphase SPH and LBM approaches for the simulation of intermittent flows

Thomas Douillet-Grellier, Sébastien Leclaire+3 more|ArXiv.org|Mar 4, 2019

Lattice Boltzmann Simulation Studies102 references20 citations

TL;DR

This study compares multiphase Smoothed Particle Hydrodynamics (SPH) and Lattice Boltzmann Method (LBM) for simulating intermittent slug flows in pipes, using continuum surface force (SPH) and color gradient (LBM) models for surface tension. LBM shows higher accuracy and speed, while SPH is more robust for high density ratios and unstable at low viscosities, with LBM being less stable at high Reynolds numbers.

ABSTRACT

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.

Motivation & Objective

• To quantitatively compare SPH and LBM for simulating intermittent two-phase flows, particularly slug flows in pipes.
• To evaluate the performance of SPH with the continuum surface force model and LBM with the color gradient method in handling surface tension.
• To assess robustness, accuracy, stability, and computational efficiency of both methods across varying density and viscosity ratios.
• To extend LBM boundary conditions to handle inlet/outlet flow conditions in multiphase systems.
• To provide practical recommendations for method selection based on flow regime and physical parameters.

Proposed method

• Implementation of SPH using the continuum surface force (CSF) model for surface tension in multiphase flows.
• Implementation of LBM using the color gradient method for surface tension in multiphase flows.
• Use of Zou-He boundary conditions extended for multiphase flows to enable velocity inlet and pressure outlet conditions.
• Simulation of static bubble test cases with varying density and viscosity ratios to validate both methods.
• Numerical simulation of 2D slug flows in pipes at multiple Reynolds numbers to assess dynamic behavior and pattern formation.
• Performance benchmarking using a shared Fortran framework with OpenMP parallelization to compare computational speed.

Experimental results

Research questions

• RQ1 How do SPH and LBM compare in simulating static bubbles with varying density and viscosity ratios?
• RQ2 Which method better captures slug flow formation and morphology in 2D pipe flows under periodic boundary conditions?
• RQ3 How do the two methods perform in terms of accuracy, stability, and convergence order at increasing Reynolds numbers?
• RQ4 What are the differences in computational efficiency and scalability between SPH and LBM for the same simulation setup?
• RQ5 How do boundary conditions affect slug frequency and size in SPH versus LBM simulations?

Key findings

• LBM achieves higher accuracy and better order of convergence than SPH, particularly in static bubble and slug flow simulations.
• SPH is more robust than LBM for high density ratios (up to 1000), while LBM struggles with high viscosity ratios.
• LBM is approximately four times faster than SPH on the same hardware for a 40,000-particle simulation, due to its local lattice-based algorithm.
• SPH produces noisier pressure fields due to Lagrangian particle motion, while LBM provides smoother pressure fields.
• LBM exhibits instability at high Reynolds numbers (Re > 1000), whereas SPH remains stable under the same conditions, limited only by the CFL condition.
• Despite similar slug pattern formation, SPH generates larger and more irregular bubbles than LBM, likely due to differences in boundary condition implementation.