An integrative smoothed particle hydrodynamics method for modeling cardiac function

Zhang, Chi; Wang, Jianhang; Rezavand, Massoud; Wu, Dong; Hu, Xiangyu

doi:10.1016/j.cma.2021.113847

Cited by 44 publications

(20 citation statements)

References 56 publications

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“…Following Refs. [1,52], the discretization of the mass and momentum conservation equations of Eq. ( 4) can be written in the total Lagrangian formulation as…”

Section: Total Lagrangian Formulationmentioning

confidence: 99%

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A multi-resolution SPH framework: Application to multi-phase fluid-structure interactions

Zhang¹,

Zhu²,

Hu³

2022

Preprint

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In the previous work, [1] proposed a multi-resolution smoothed particle hydrodynamics (SPH) method for fluid-structure interactions (FSI) with achieving an optimized computational efficiency meanwhile maintaining good numerical robustness and accuracy. In the present paper, this multiresolution SPH framework where different spatial-temporal discretizations are applied for different sub-systems is extended to multi-phase flows involving large density ratio and interacting with rigid or flexible structure. To this end, a simple and efficient multi-phase model is introduced by exploiting different density reinitialization strategies other than applying different formulations to implement mass conservation to the light and heavy phases, respectively, to realize the target of using same artificial speed of sound for the both. To eliminate the unnatural voids and unrealistic phase separation meanwhile decrease the numerical dissipation, the transport velocity formulation are rewritten by applying temporal local flow state dependent background pressure. To handle the FSI coupling in both single-and multi-resolution scenarios in the triple point, the one-sided Riemann-based solid boundary condition is adopted. A set of examples involving multi-phase flows with high density ratio and complex interface and multi-phase FSI are studied to demonstrate the efficiency, accuracy and robustness of the present method. The validations presented herein and those reported in the original paper of [1] where single-phase FSI is studied put the present multi-resolution SPH framework in good stead in terms of computational efficiency for multi-physics applications.

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“…Following Refs. [1,52], the discretization of the mass and momentum conservation equations of Eq. ( 4) can be written in the total Lagrangian formulation as…”

Section: Total Lagrangian Formulationmentioning

confidence: 99%

“…It is worth noting that the rate of change for deformation gradient dF dt is computed through [52] dF…”

Section: Time Integrationmentioning

confidence: 99%

A multi-resolution SPH framework: Application to multi-phase fluid-structure interactions

Zhang¹,

Zhu²,

Hu³

2022

Preprint

Self Cite

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show abstract

“…However, extra computational efforts are induced due to the interpolation and matrix inverse for each particle at every time step. On the other hand, this kernel gradient correction is widely applied in the total Lagrangian formulation as it only to be calculated once at the initial reference configuration [38,39,40] which will be presented in details in Section 4.…”

Section: Kernel Gradient Correctionmentioning

confidence: 99%

“…Compared with the UL formulation, the TL formulation shows promising potential in the simulation of finite deformation due to its attractive advantages in being free from tensile instability and ensuring 1st-order consistency when computing deformation gradient by introducing the kernel gradient correction. Since its inception, it has been applied for the problems of necking and fracture in thermomechanical deformations [143], fluid-structure interaction (FSI) [13,144,14,145] and biomechanics [146,22], among many others. In this paper, we focus on the TL formulation with highlights on stablized term, the steady state solution and the hourglass control scheme.…”

Section: Solid Mechanicsmentioning

confidence: 99%

“…As a fully Lagrangian meshless method, whereby a set of particles are introduced to discretize the continuum media and their interactions determined by a Gaussianlike kernel function to approximate the mechanics, the smooth particle hydrodynamics (SPH) [1,2] has been demonstrated to be a compromising alternative of meshbased methods and received significant interest in the past decades [3,4,5,6]. Thanks to its Lagrangian feature, the SPH method has shown peculiar advantages in handling free-surface flows [7,8] involving violent impact and breaking events [9], structure analysis with crack propagation and large deformation [4,10,11] and multi-physics problems [12] including fluid-structure interactions (FSI) [13,14,15], multi-phase flows [16,17,18], additive manufacturing [19,20] and cardiac modeling [21,22,23], and comprehensive reviews can be found in recent Refs. [9,14,24,25,26,27,28].…”

Section: Introductionmentioning

confidence: 99%

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Review on Smoothed Particle Hydrodynamics: Methodology development and recent achievement

Zhang¹,

Zhu²,

Wang³

et al. 2022

Preprint

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Since its inception, the full Lagrangian meshless smoothed particle hydrodynamics (SPH) method has experienced a tremendous enhancement in methodology and impacted a range of multi-physics applications in science and engineering. The paper presents a concise review on latest developments and achievements of the SPH method, including (1) brief review of theory and fundamental with kernel corrections, (2) the Riemann-based SPH method with dissipation limiting and high-order data reconstruction by using MUSCL, WENO and MOOD schemes, (3) particle neighbor searching with particle sorting and efficient dual-criteria time stepping schemes, (4) total Lagrangian formulation with stablized, dynamics relaxation and hourglass control schemes, (5) fluid-structure interaction scheme with interface treatments and multi-resolution discretizations, (6) novel applications of particle relaxation for mesh and particle generations. Last but not least, benchmark tests for validating computational accuracy, convergence, robustness and efficiency are also supplied accordingly.

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Unified non-hourglass formulation for total Lagrangian SPH solid dynamics

Wu,

Tang,

Zhang

et al. 2024

Comput Mech

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The persistence of hourglass modes poses a significant numerical instability issue in total Lagrangian smoothed particle hydrodynamics (TLSPH) solid dynamics, especially when dealing with substantial deformations, regardless of material properties. However, existing hourglass control methods have shown effectiveness only within limited applications. Thus far, a comprehensive solution capable of addressing hourglass issues across a wide range of material models, including elasticity, plasticity, and anisotropy, remains elusive. In this study, we introduce a unified TLSPH formulation grounded in volumetric-deviatoric stress decomposition, aimed at fundamentally mitigating hourglass modes in general simulations. Different conceptually from previous approaches using stress points or extra viscous or hourglass-control stresses within the momentum equation, our formulation is based on the weighted average of a standard but hourglass-prone formulation and an essentially non-hourglass formulation for elastic materials, employing a single limiter to dynamically adjust the weighting between the two formulations. Crucially, the dimensionless characteristic of the formulation enables seamless handling of complex material models. To validate the effectiveness of our formulation, we conduct simulations across a range of benchmark cases involving elastic, plastic, and anisotropic materials. To illustrate its versatility, we apply the formulation to simulate a complex scenario involving viscous plastic Oobleck material, contacts, and very large deformation. Our work addresses a critical gap in TLSPH simulations by offering a unified approach to mitigate hourglass modes, enhancing the reliability and accuracy of simulations across diverse material models and complex scenarios.

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An integrative smoothed particle hydrodynamics method for modeling cardiac function

Cited by 44 publications

References 56 publications

A multi-resolution SPH framework: Application to multi-phase fluid-structure interactions

A multi-resolution SPH framework: Application to multi-phase fluid-structure interactions

Review on Smoothed Particle Hydrodynamics: Methodology development and recent achievement

Unified non-hourglass formulation for total Lagrangian SPH solid dynamics

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