An efficient implementation of the bidirectional buffer: towards laminar and turbulent open-boundary flows

TL;DR

This paper tackles open-boundary challenges in particle-based SPH simulations, especially backflow and multiple inlets/outlets, by introducing three targeted improvements within the WCSPH-RANS framework. It implements (i) a continuum-hypothesis–based fringe to preserve buffer consistency, (ii) unique buffer IDs with containment checks to ensure buffer independence, and (iii) RKGC with a mirror boundary to achieve first-order accuracy near open boundaries. The authors validate the approach on laminar/turbulent straight and U-shaped channels, laminar/turbulent plane jets in compact domains, and a 3D self-rotational micro-mixer, demonstrating improved stability, accuracy, and computational efficiency. Overall, the work extends the applicability of WCSPH-RANS to complex open-boundary flows and enables accurate simulations in substantially smaller domains than traditional mesh-based methods.

Abstract

To effectively handle flows characterized by strong backflow and multiple open boundaries within particle-based frameworks, this study introduces three enhancements to improve the consistency, independence, and accuracy of the buffer-based open boundary condition in SPHinXsys. First, to improve the buffer consistency, the continuum hypothesis is introduced to prevent the excessive particle addition induced by strong backflow. Secondly, the independence of the bidirectional buffer is enhanced through region-constrained and independent labeling schemes, which effectively eliminate buffer interference and erroneous particle deletion in complex open-boundary flows. Thirdly, the original zeroth-order consistent pressure boundary condition is upgraded to first-order consistency by introducing a mirror boundary treatment for the correction matrix. The implementation is based on the rigorously validated weakly compressible smoothed particle hydrodynamics coupled with Reynolds-averaged Navier-Stokes (WCSPH-RANS) method, and both laminar and turbulent flow simulations are performed. Four test cases, including straight and U-shaped channel flows, a plane jet, and the flow in a 3D self-rotational micro-mixer, are conducted to comprehensively validate the proposed improvements. Among these cases, the turbulent plane jet is successfully simulated at a moderate resolution within a very compact computational domain involving strong backflow, a condition that is usually challenging for mesh-based methods. The three improvements require only minor modifications to the code framework, yet they yield significant performance gains.

Figures (26)

• Figure 1: (a) The determination of the buffer regions by cell link list. (b) The concept of the particle treatment of the local-relabeling-based open boundary strategy at a specific time instant $T$ when both the inflow and outflow occur. This illustration is based on a straight channel flow. The red dot lines refer to the relabeling boundaries, and the blue regions are the buffer regions.
• Figure 2: (a) Configuration of a whole particle array, and (b) the outflow steps when the particle 6 outflows.
• Figure 3: The continuous trajectory of a buffer particle $i$ located near the relabeling boundary and influenced by the backflow: (a) without the proposed improvement; (b) with the proposed improvement.
• Figure 4: (a) Without unique buffer IDs, particle deletion errors may occur due to interference; (b) with unique buffer IDs, erroneous deletion is avoided.
• Figure 5: When the two buffer regions are vertically stacked, (a) interference occurs along $y$ direction; (b) interference is avoided after adding the contain-checking.