Excessive nonphysical energy dissipation is a problem in Smoothed Particle Hydrodynamics (SPH) when modeling free surface waves, resulting in a significant decrease in wave amplitude within a few wavelengths for progressive waves. This dissipation poses a limitation to the physical scale of SPH applications involving water wave propagation. Some prior solutions to this wave decay problem rely on elaborate schemes, which require a complex, or non-straightforward, implementation. Other approaches demand large smoothing lengths that lead to longer simulation times and potential degradation of the results. In this work we present an approach based on a kernel gradient correction. Our scheme is fully 3D and solves the main known drawbacks of kernel gradient corrections, such as instabilities and lack of momentum conservation. The latter is ensured by adopting an averaged correction matrix, so as to conserve reciprocity during particle interactions. We test our model with a standing wave in a basin and a progressive wave train in a wave tank, and in both cases no nonphysical decay occurs. A comparison to an approach based on large smoothing factors shows advantages both in quality of the results and simulation time.

在建模自由表面波时，平滑粒子流体动力学 (SPH) 中存在过多的非物理能量耗散问题，这会导致渐进波在几个波长内的波幅显着降低。这种耗散对涉及水波传播的 SPH 应用的物理规模构成了限制。这个波衰减问题的一些先前解决方案依赖于复杂的方案，这需要复杂的或非直接的实现。其他方法需要大的平滑长度，这会导致更长的模拟时间和结果的潜在劣化。在这项工作中，我们提出了一种基于内核梯度校正的方法。我们的方案是完全 3D 的，解决了核梯度校正的主要已知缺点，例如不稳定性和缺乏动量守恒。后者通过采用平均校正矩阵来保证，从而在粒子相互作用过程中保持互易性。我们用盆地中的驻波和波浪池中的渐进波列测试我们的模型，在这两种情况下都没有发生非物理衰减。与基于大平滑因子的方法的比较显示了结果质量和仿真时间方面的优势。