Since its introduction in 1977, Smoothed Particle Hydrodynamics (SPH) has evolved from a numerical method developed for astrophysical simulations into a versatile computational framework used across a broad range of scientific and engineering disciplines. Its continued development has brought significant advances in numerical formulations, physical modeling, computational efficiency, and practical applications. Despite this progress, important challenges remain before SPH can fully realize its potential as a robust, accurate, and widely applicable simulation method.
The SPHERIC Grand Challenges were originally introduced in 2014 to identify the fundamental limitations of the method and establish shared research priorities for the entire SPH community. Over the years, substantial progress has been made in several of these areas, while new opportunities and challenges have emerged, driven by advances in computational hardware, multiphysics modeling, adaptive algorithms, and artificial intelligence.
​Recognizing these developments, the SPHERIC Steering Committee has undertaken a comprehensive revision of the Grand Challenges in 2026, resulting in five updated priorities that reflect the current state of the art and the future directions of SPH research. The new list is:
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Grand Challenge 1: Mathematical and Numerical Foundations (GC1)
Advance the SPH mathematical and numerical foundations by addressing fundamental challenges related to conservation, convergence, consistency, and stability. Special emphasis is placed on developing rigorous theoretical frameworks and robust numerical formulations that improve the accuracy, reliability, and predictability of SPH simulations. This includes the development of consistent discretization schemes, stable numerical algorithms, and accurate, generalizable boundary treatments capable of handling complex geometries and physical conditions.
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Grand Challenge 2: Advanced Physical and Multi-Physics Modeling (GC2)
Extend the capabilities of SPH to accurately represent complex physical phenomena and their interactions across multiple spatial and temporal scales. Key challenges include the modeling of turbulence, phase change, surface tension and contact-line dynamics, heat transfer, fracture mechanics, heterogeneous materials, and magnetohydrodynamics. Addressing these challenges requires the development of advanced physical models and robust multi-physics coupling strategies that preserve the underlying physical principles while enabling reliable simulations of increasingly complex systems.
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Grand Challenge 3: Efficient and Intelligent Algorithms (GC3)
Develop efficient and intelligent computational approaches that enhance the accuracy, flexibility, and computational efficiency of SPH simulations. Research directions include adaptive spatial and temporal resolution strategies, hybrid numerical methods and coupled schemes that combine SPH with complementary modeling approaches, and reduced-order models for accelerating complex simulations. Other aspects include the integration of artificial intelligence and data-driven techniques for algorithm optimization, computational acceleration, and improved predictive capabilities, while maintaining physical consistency and numerical reliability.
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Grand Challenge 4: High-Performance and Heterogeneous Computing (GC4)
Advance the computational scalability and performance of SPH to enable increasingly large and complex simulations on modern and emerging computing architectures. Key challenges include the development of scalable parallel algorithms, efficient utilization of multi-accelerator systems, and effective deployment across distributed heterogeneous computing environments. Research efforts should also address memory management, data communication and I/O optimization, code portability across hardware platforms, and energy-efficient execution. These developments are essential for exploiting next-generation high-performance computing systems and preparing SPH for exascale computing.
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Grand Challenge 5: Scientific and Engineering Applications (GC5)
Expand the scientific and engineering impact of SPH by addressing challenging real-world problems across a broad range of disciplines and industrial applications. Particular emphasis should be placed on large-scale and complex engineering systems, the integration of numerical simulations with experimental measurements and field observations, and the establishment of rigorous validation and benchmarking methodologies. Strengthening collaboration between academia, industry, and other stakeholders is essential to promote the transfer of knowledge, accelerate the adoption of SPH technologies, and demonstrate their practical relevance and societal impact.
 
These five Grand Challenges are not intended as an exhaustive or definitive roadmap, but rather as a living document that encourages discussion, collaboration, and continued progress across the SPH community. Their interconnected nature highlights the importance of advancing numerical accuracy, physical fidelity, computational efficiency, and practical applicability together.​ 
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The Grand Challenges list presented above supersede the previous list, which is retained below for historical reference and to document the evolution of research priorities within the SPH community. Researchers and practitioners are encouraged to contribute suggestions, identify emerging challenges, and help keep this collective vision relevant as the field continues to evolve.