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A hydroelastic fluid–structure interaction (FSI) solver entirely based on the Riemann-SPH method is proposed. In this scheme, the Riemann-SPH method is incorporated to model elastic structures, which is performed by proposing a new treatment on Cauchy stress. The present structure solver can avoid the use of the artificial viscous force and can obtain good results. For the fluid, the conventional Riemann-SPH with a low-dissipation limiter is adopted to simulate incompressible free surface flows. The structure solver is coupled with the fluid solver by a simple coupling way considering the force balance. The developed structure solver is verified by three benchmarks, namely a free oscillating cantilever plate, stress concentration problem of a plate and wave propagation in a cable. Subsequently, through several 2D and 3D typical hydroelastic FSI tests, the accuracy and robustness of the present FSI solver are verified/validated by comparing with analytical solutions and experimental results. • The Riemann-SPH method is incorporated to be an elastic structure solver. • A unified hydroelastic FSI solver based on the Riemann-SPH method is proposed. • The present FSI solver can reproduce typical FSI problems with superior accuracy. [ABSTRACT FROM AUTHOR]

There are many compressible flows involving strong discontinuities in nature and engineering applications. Their behaviors are complicated by the existence of shock waves, rarefaction waves and contact discontinuities. To investigate these flows, a shock-capturing scheme based on smoothed particle hydrodynamics (SPH) is proposed. In this scheme, Roe's approximate Riemann solver cooperated with a novel limiter is embedded into the SPH governing equations to capture shocks. This limiter is simple and effective to control numerical dissipations, and the use of this limiter eliminates the tunable artificial viscosity as required by the conventional SPH. Additionally, to restore the accuracy limited by heterogeneous particle distribution that is usually encountered in the simulation of strongly-compressible flows, the gradient operator in the continuity equation is corrected by a renormalization procedure. Last but not least, for initial particle distribution, unlike the equal mass particle distribution commonly used in compressible SPH simulations, the equal spacing particle distribution is adopted in this scheme, which makes it much easier to model multidimensional problems. The present scheme has been verified by a set of benchmark tests involving contact discontinuities, extreme shock waves and strong rarefaction waves, some of which are firstly simulated by the SPH method. • An accurate shock-capturing SPH scheme is proposed to simulate compressible flows. • A novel dissipation limiter is designed for Riemann-SPH to adjust dissipations. • The proposed scheme can capture sharp shock waves. [ABSTRACT FROM AUTHOR]

In the past few decades, the weighted essentially non-oscillatory (WENO) scheme has been widely used in mesh-based methods and has achieved great success, but its application to the smoothed particle hydrodynamics (SPH) is still limited. In this paper, a simple and accurate implementation of the WENO scheme to the SPH method is proposed for solving compressible flows with discontinuities and small-scale structures. In the proposed scheme, several equal spacing points along the line joining two interacting particles are selected to constitute candidate stencils. However, due to the Lagrangian characteristic of SPH, some points may be lost. To solve this problem, we first search the particles closest to these missing points, and then the first-order Taylor series expansion is used to obtain the corresponding primitive variables of these points. After that, through the WENO strategy, the left and right states at the interface between two interacting particles are reconstructed. Finally, the inter-particle interactions are determined by using Roe's approximate Riemann solver. Several numerical tests show that the proposed WENO-SPH method is robust and able to accurately capture shockwaves, and benefiting from the low-dissipation property, it also has a good performance in resolving small-scale structures in flows. • A new WENO-SPH method is proposed for compressible flows with discontinuities. • The convergence of the WENO-SPH is studied by reconstructing a simple function. • The accuracy of the WENO-SPH is validated through several numerical tests. [ABSTRACT FROM AUTHOR]

In this work, a particle regeneration technique is developed for Smoothed Particle Hydrodynamics (SPH). In traditional SPH, the particle disorder phenomenon will occur when dealing with the strongly compressible flow problem. To solve this, in the present work, uniformly distributed background particles filled in the computational domain are adopted. The particle regeneration technique is that the fluid particles replaced by the background particles when the fluid density changes to a specific limitation. The fluid variables of the background particles are approximated by the fluid variables of the initial particles in their support domain. For the multiphase flow, the multiphase interface is calculated by an interface reproducing algorithm, in which, we defined an indicator variable, and set the indicator value discontinuity between different materials. By setting the threshold value, the multiphase interface is reconstructed. Meanwhile, the momentum equation for the Riemann SPH is modified to eliminate the instability in the light phase. Several numerical examples are studied to verify the present algorithm. [ABSTRACT FROM AUTHOR]

In this work, we proposed a meshfree crack propagation algorithm for dynamic fracture in arbitrary curved shell structures. In the numerical simulation of shell fracture, the treatment of crack discontinuity and simulation of fracture fragments are involved. In meshfree methods, since the connection between particles can be changed easily, which makes it suitable for dealing with such problems. In this study, firstly, the crack initiation algorithm for both ductile and brittle material is proposed based on the damage evolution. Besides, in the simulation, we assume that the crack tip coincides with the stress point, which means that the crack tip moves from one stress point to another, and by connecting the crack tip, the crack path is generated. Then a 3D visibility criterion for arbitrary curved shell structures is established, based on which the support domain of stress points is cut by the crack path to model the crack discontinuity. Finally, the crack propagation algorithm for dynamic fracture in curved shells is established; several numerical examples are studied to verify the reliability of the proposed algorithm. • Propose a 3D meshfree crack propagation algorithm for dynamic fracture in curved shells. • The damage constitutive model for shell structures is proposed. • Crack initialization is achieved based on the damage evolution. • Establish an efficient 3D visibility criterion for the arbitrary curved shell. • Corrected material parameters in the damage model eliminate 'Mesh sensitivity' problem. [ABSTRACT FROM AUTHOR]

3-D SPH simulations are often time-consuming due to the massive particle numbers. For the problem which has axisymmetric characteristics, the solving of the entire three-dimensional domain can be simplified which saves computational cost dramatically. In this paper, a novel derivation for the SPH formulation in cylindrical coordinate is presented, which is straightforward and physically meaningful. A multiphase numerical model is developed based on the derived formulation including the discretization formulas of surface tension force, viscous force, interface sharpness force and the treatment of high density ratio near the multiphase interface, as well as an improved anti-penetration treatment close to the axis. The effectiveness and robustness of the proposed multiphase SPH model are demonstrated via the classical surface-tension test and bubble rising problems at different conditions. The results are compared with analytical solutions, the experimental data and other numerical results. The promising results of the novel axisymmetric SPH model demonstrate a great potential for an efficient SPH modeling of complex axisymmetric multiphase flows. Dramatic efficiency boost is achieved by comparing the axisymmetric simulation with 3-D simulation in terms of CPU time. • This article is dedicated to the improvement of SPH in cylindrical coordinate. • A novel derivation of axisymmetric SPH formulation is presented. • A multiphase model based on axisymmetric SPH is developed. • The newly proposed axisymmetric SPH formulas can simulate fully developed multiphase flows. • Large efficiency boost is observed when comparing with purely 3-D simulations. [ABSTRACT FROM AUTHOR]

The present work targets a high-order SPH scheme for simulating incompressible flows. To achieve this, typical spatial reconstructions, piecewise constant approximation, MUSCL, WENO and TENO techniques are employed in the Riemann-SPH formulation. These reconstructions are based on primitive variables rather than numerical fluxes, and the advection term is not altered. Therefore, the polynomial coefficients and the optimal weights in the W/TENO reconstruction are corrected to adapt this system. The accuracy of SPH is improved by W/TENO reconstruction up to 4th and 5th order in the Eulerian framework, respectively. The performances in the Lagrangian, ALE and Eulerian frameworks, and of different reconstructions are also compared. TENO-SPH can obtain comparable results with half (or even lower) of the particle resolution as compared to previous SPH versions. Moreover, the constraint of mass change related to the volume conservation and pressure instabilities is investigated in the Eulerian framework. [ABSTRACT FROM AUTHOR]

A multiphase SPH model based on Roe's approximate Riemann solver is proposed to simulate complex interfacial flows in hydraulics. In this multiphase model, the solution to a one-dimensional Riemann problem is introduced into the SPH governing equations to determine the interaction between particles. The Riemann problem is solved by Roe's approximate Riemann solver which may introduce excessive numerical dissipations. To reduce these dissipations, a dissipation limiter is applied. An equivalent relation between the dissipation term in the dissipation limiter and the Reynolds number is derived to model viscous flows of different Reynolds numbers. For flows of high density ratios (up to 1000), stable and smooth interfacial pressure can be obtained. The realistic compressibility can be considered for the light fluid and a larger time step can be allowed, leading to a decrease of the computational cost. To further make the simulation more efficient, an optimized adaptive linked-list search algorithm is introduced. Using this optimized algorithm, the particle interaction list can be updated every dozen of time steps instead of at each time step, which contributes to a significant reduction of the total computational cost. Seven numerical tests are presented to validate this multiphase model. • A multiphase SPH model based on Roe's approximate Riemann solver is proposed to simulate complex hydraulic flows. • A dissipation limiter is applied to adjust numerical dissipations introduced by Roe's approximate Riemann solver. • An equivalent relation between the dissipation term in the dissipation limiter and the Reynolds number is derived. • For flows with high density ratios, stable and smooth interfacial pressure can be obtained. • An optimized adaptive linked-list search algorithm is presented to save computational cost. [ABSTRACT FROM AUTHOR]

This paper presents an improved particle shifting technology (IPST) for smoothed particle hydrodynamics (SPH). It allows particles in the vicinity of the free-surface to be shifted in all the directions in case they are not uniformly distributed, rather than just shifted tangentially to the free-surface in some conventional particle shifting technologies. Therefore, with the new technique, the imprecise shifting due to the inaccurate evaluations of the local normal and tangential vectors of the free-surface can be avoided, and a more uniform particle distribution near the free-surface can be obtained even for long-term simulations, which improves the accuracy and stability of the SPH method. Besides, by combining the advantages of two existing free-surface detection methods, an optimized detection approach is provided. It is capable of detecting the free-surface particles accurately, and meanwhile, it is easier to implement and requires lower computational costs, especially for three-dimensional problems. Several numerical tests show that the proposed IPST and the optimized free-surface detection method are robust and accurate for the simulation of a variety of free-surface flows. • An improved particle shifting technology (IPST) in the SPH method is proposed. • An optimized free-surface detection method in SPH is introduced. • The accuracy and robustness of the proposed IPST is validated on several long-term simulations. [ABSTRACT FROM AUTHOR]

A coupling approach of the isogeometric–meshfree method and the peridynamic method is developed for static and dynamic crack propagation. The coupling approach exhibits advantages in the flexibility of modeling cracks and the exactness of geometry representation. The isogeometric–meshfree method, which adopts the moving least-squares approximations to establish the equivalence between meshfree shape functions and isogeometric basis functions, is capable of obtaining the exact geometry. The isogeometric–meshfree nodes located on the geometry can be directly coupled with peridynamic points by the balanced force principle, which is straightforward and effective. With this approach, the boundary conditions can be enforced directly using the isogeometric–meshfree method, and the surface effects of peridynamics are effectively eliminated. Moreover, the present approach is flexible in switching the isogeometric–meshfree nodes to peridynamic points and achieving adaptive coupling with the same convergence rate as the one for the isogeometric–meshfree method, which is higher than the one for the original peridynamic method. The dual-horizon peridynamic method is adopted for non-uniform discretization. Based on the exact geometry representation, the coupling approach is further extended to crack problems with contact loading. Several representative examples are presented to validate the effectiveness of the present approach in solving static/dynamic crack problems and studying fractures caused by contact. • A coupling approach of the IGAMF method and PD is developed for crack propagation. • The present method can switch the IGAMF nodes to PD points for adaptive coupling. • The coupling approach demonstrates a higher convergence rate than PD. • The surface effects of PD are effectively eliminated. [ABSTRACT FROM AUTHOR]

This work presents a multi-resolution fluid–structure interaction (FSI) solver for hydroelastic issues by coupling the Weakly Compressive Smoothed Particle Hydrodynamics (WCSPH) method and the Finite Element Method (FEM). The fluid is simulated by the SPH method, and the structure response is considered by the FEM beam. The normal flux method is employed to calculate the coupled force between the fluid and structure by considering the surface integration term in SPH approximation equations. A multi-resolution technology is proposed by discretizing the fluid and structure with different resolutions. The resolution of beam elements can be either coarser or finer than that of SPH particles. Finally, the accuracy, robustness and efficiency of the current FSI solver are strictly validated by several typical benchmarks, including the hydrostatic, free-surface flow and water entry problems. • We developed a coupled SPH-FEM method for fluid–structure interactions. • Different spatial–temporal resolution is employed for fluid and solid structure. • The accuracy, efficiency, and robustness of the FSI solver are strictly validated. [ABSTRACT FROM AUTHOR]

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]