High-order multidimensional gradient operator in smoothed particle hydrodynamics

Title	High-order multidimensional gradient operator in smoothed particle hydrodynamics
Authors	O. P. Stoyanovskaya¹ ¹National Research Mordovia State University
Annotation	The paper generalizes the discrete differentiation operator for smoothed particle hydrodynamics, which in the one-dimensional case together with high-order kernels forms a T-stable method, to a space of any dimension. Computational experiments show that the projected 4th order of gradient approximation is achieved in practice.
Keywords	smoothed particle hydrodynamics, T-stability, high-order kernels, Wendland polynomials
Citation	Stoyanovskaya O. P. ''High-order multidimensional gradient operator in smoothed particle hydrodynamics'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 29-31, 2025). Saransk: SVMO Publ, 2025. - pp. 239-241. Available at: https://conf.svmo.ru/files/2025/papers/paper48.pdf. - Date of access: 30.08.2025.