The Arbitrary Lagrangian–Eulerian Smoothed Particle Hydrodynamics (ALE-SPH) formulation can guarantee stable solutions preventing the adoption of empirical parameters such as artificial viscosity. However, the convergence rate of the ALE-SPH formulation is still limited by the inaccuracy of the SPH spatial operators. In this work, a Weighted Essentially Non-Oscillatory (WENO) spatial reconstruction is then adopted to minimise the numerical diffusion introduced by the approximate Riemann solver (which ensures stability), in combination with two alternative approaches to restore the consistency of the scheme: corrected divergence SPH operators and the particle regularisation guaranteed by the correction of the transport velocity. The present work has been developed in the framework of the DualSPHysics open-source code. The beneficial effect of the WENO reconstruction to reduce numerical diffusion in ALE-SPH schemes is first confirmed by analysing the propagation of a small pressure perturbation in a fluid initially at rest. With the aid of a 2-D vortex test case, it is then demonstrated that the two aforementioned techniques to restore consistency effectively reduce saturation in the convergence to the analytical solution. Moreover, high-order (above second) convergence is achieved. Yet, the presented scheme is tested by means of a circular blast wave problem to demonstrate that the restoration of consistency is a key feature to guarantee accuracy even in the presence of a discontinuous pressure field. Finally, a standing wave has been reproduced with the aim of assessing the capability of the proposed approach to simulate free-surface flows.

任意拉格朗日-欧拉平滑粒子流体动力学 (ALE-SPH) 公式可以保证稳定的解决方案，防止采用人工粘度等经验参数。然而，ALE-SPH 公式的收敛速度仍然受到 SPH 空间算子的不准确性的限制。在这项工作中，然后采用加权本质非振荡（WENO）空间重建来最小化近似黎曼求解器引入的数值扩散（这确保了稳定性），并结合两种替代方法来恢复方案的一致性：散度SPH算子和通过传输速度校正保证的粒子正则化。目前的工作是在 DualSPHysics 开源代码框架下开发的。通过分析初始静止流体中小压力扰动的传播，首先证实了 WENO 重建对减少 ALE-SPH 方案中的数值扩散的有益效果。借助二维涡流测试用例，证明上述两种恢复一致性的技术有效地降低了解析解收敛的饱和度。此外，还实现了高阶（二阶以上）收敛。然而，通过圆形冲击波问题对所提出的方案进行了测试，以证明即使在存在不连续压力场的情况下，一致性的恢复也是保证精度的关键特征。最后，再现了驻波，目的是评估所提出的方法模拟自由表面流的能力。