Challenges in Meshfree Methods: Addressing the Shortcomings of Smoothed Particle Hydrodynamics (SPH)

The development of meshfree methods, particularly Smoothed Particle Hydrodynamics (SPH), has made significant progress in recent years. However, despite these advances, SPH still faces numerous challenges that hinder its widespread adoption as a reliable and efficient numerical tool. The purpose of this article is to highlight the key issues that need to be addressed in order to overcome these hurdles and establish SPH as a mature method.

One of the primary concerns with SPH is its lack of broad recognition from the scientific community as a serious candidate for numerical simulation. This is due, in part, to the unknown properties of the method and the many unanswered questions that remain on purely theoretical grounds. To address this challenge, researchers must focus on clarifying the most important problems remaining in the development of SPH, listing significant publications on each topic, and keeping aware of the state-of-the-art.

Another critical issue is the need for improved convergence, consistency, and stability in SPH simulations. This requires a better understanding of the method's numerical properties, including boundary conditions, kernel properties, and time marching. Furthermore, researchers must also investigate the existence and properties of solutions to ensure that the method is capable of producing accurate and reliable results.

One of the main reasons why SPH has not yet achieved widespread acceptance as a numerical tool is its lack of maturity. This is reflected in the numerous open questions and challenges that remain to be addressed. For example, researchers must still grapple with issues related to kernel properties, boundary conditions, and time marching, which can significantly impact the accuracy and efficiency of SPH simulations.

To overcome these challenges, it is essential to foster cooperation among research teams and establish a living network of experts working on SPH development. This can be achieved through the creation of a working group, such as the SPHERIC Grand Challenge Working Group (GCWG), which brings together researchers from around the world to share knowledge, clarify needs, and identify active research areas.

In conclusion, addressing the challenges in meshfree methods, particularly SPH, is crucial for advancing our understanding of complex physical phenomena. By clarifying the most important problems remaining in SPH development, listing significant publications on each topic, and keeping aware of the state-of-the-art, researchers can help establish SPH as a mature method capable of producing accurate and reliable results.

Challenges in meshfree methods