Higher-order nonlocal theory of Updated Lagrangian Particle Hydrodynamics (ULPH) and simulations of multiphase flows.

In this work, we present a higher-order nonlocal continuum theory of a recently developed updated Lagrangian particle hydrodynamics (ULPH) (see: Tu and Li, 2017 and Yan et al., 2019) and its applications to multiphase flows. The original nonlocal differential operators used in ULPH have only the first-order accuracy, and they may not be able to simulate some complicated and delicate three-dimensional flow problems. In order to improve the computational accuracy and stability, we adopt the nonlocal synchronized differential operator from the reproducing kernel particle method (RKPM), which is regarded as the higher-order nonlocal differential operator, and we apply them to build higher-order ULPH formulations. The main advantage of the higher-order nonlocal differential operator over the original one is its high accuracy in unstructured particle distribution, and it is fully controlled by the approximation polynomial basis. Numerical verifications have been carried out to validate the accuracy of the proposed approach by using various polynomial bases. Several challenging and delicate three-dimensional multiphase flow benchmark problems are solved to demonstrate the capability of the proposed method. The numerical results of the higher-order ULPH show good agreement with theoretical and numerical solutions in the literature, demonstrating the promising potential of higher-order nonlocal ULPH formulation in modeling and simulating multiphase flows with substantial topological variations of interfaces and high density ratios. • We have shown in the first time that the particle nonlocal differential operators are originated from RKPM. • We have developed a higher-order nonlocal ULPH theory and its computation formulations. • We have employed the higher-order nonlocal ULPH to model and simulate 3D multiphase flow computations. [ABSTRACT FROM AUTHOR]