Journal of Computational Physics最新文献_第4页

Three-dimensional soft discrete element method for large-scale simulations of soft spheres 三维软离散元法在软球体大尺度模拟中的应用

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-01-12 DOI: 10.1016/j.jcp.2026.114681

Zonglin Li , Ju Chen , Qiang Tian , Haiyan Hu

Soft particles are ubiquitous in both nature and industries, yet existing three-dimensional simulation methods remain inefficient. This paper presents a three-dimensional soft discrete element method (3D SDEM) for the efficient large-scale dynamic simulations of soft spherical particles. In the method, each soft sphere is modeled as a truncated ellipsoid with a homogeneous strain field, which requires 12 degrees of freedom only. The dynamic equations of soft spheres are derived by using the Lagrange-d’Alembert principle, and the contact detection between soft spheres is handled via the Common Normal Method. The contact force model and the strain energy function are formulated and validated through various compression scenarios of a single soft sphere. The accuracy and efficiency of the 3D SDEM are verified through two-sphere collision simulations and three-dimensional soft sphere compaction simulations. Notably, the compression of 10,000 soft spheres from a jammed state to 95 % volume fraction is simulated within five hours on a laptop computer with a single GPU only. Finally, the method is used to simulate the shear flow of soft particle glasses comprising 1000 soft spheres and successfully capture individual soft sphere deformations not reported before. These results demonstrate that the 3D SDEM enables the efficient modeling of large-scale soft sphere systems, paving the way for advanced studies in both physics and engineering applications.

软粒子在自然界和工业中无处不在，但现有的三维模拟方法仍然效率低下。本文提出了一种三维软离散元法（3D SDEM），用于软球形颗粒的大规模动态模拟。该方法将每个软球建模为具有均匀应变场的截断椭球体，只需要12个自由度。利用拉格朗日-达朗贝尔原理推导了软球的动力学方程，利用公法向法处理了软球之间的接触检测。建立了接触力模型和应变能函数，并通过对单个软球的不同压缩情况进行了验证。通过双球碰撞仿真和三维软球压实仿真，验证了三维SDEM的精度和效率。值得注意的是，在一台只有一个GPU的笔记本电脑上，可以在5小时内模拟1万个软球体从堵塞状态压缩到95%的体积分数。最后，利用该方法模拟了由1000个软球组成的软颗粒玻璃的剪切流动，成功捕获了以前未报道的单个软球变形。这些结果表明，三维SDEM能够有效地建模大型软球系统，为物理和工程应用的深入研究铺平了道路。

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引用次数: 0

On ground states of spin-1 dipolar Bose-Einstein condensate: Dimension reduction and numerical computation 自旋-1偶极玻色-爱因斯坦凝聚的基态：降维和数值计算

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-01-11 DOI: 10.1016/j.jcp.2026.114671

Zhixuan Li , Qinglin Tang , Hanquan Wang , Yong Zhang

We perform a dimension reduction for spin-1 dipolar Bose-Einstein condensate (BEC), which is described by the mean-field Gross-Pitaevskii equations (GPEs) coupled with dipole-dipole interaction (DDI), under strongly anisotropic external confining potentials. The original three dimensions (3D) problem is then reduced to quasi-2D and quasi-1D models for pancake- and cigar-shaped trapping potentials respectively. To compute the ground state, we propose an efficient and accurate algorithm by incorporating the kernel truncation method (KTM) for the dipolar potential evaluation into the projected gradient flow (PGF) method. The long-range dipolar potential is computed efficiently and accurately by KTM with optimal zero-padding factor, and the resulted PGF-KTM algorithm achieves spectral accuracy in the ground states. We compute the ground states in different space dimensions, and confirm the convergence and rates of dimension reduction from 3D to quasi-2D and from 3D to quasi-1D. Extensive numerical results of ground states for BECs with ferromagnetic/antiferromagnetic interaction and various external potentials in 1D/2D/3D are reported.

在强各向异性外约束势下，用平均场Gross-Pitaevskii方程（gpe）耦合偶极-偶极相互作用（DDI）描述自旋-1偶极玻色-爱因斯坦凝聚体（BEC），对其进行了降维。然后将原来的三维问题分别简化为饼形和雪茄形捕获势的准二维和准一维模型。为了计算基态，我们将偶极势计算的核截断法（KTM）结合到投影梯度流（PGF）方法中，提出了一种高效、准确的算法。利用最优补零因子的KTM高效、准确地计算了远距离偶极势，得到的PGF-KTM算法在基态下实现了光谱精度。我们计算了不同空间维度的基态，并确定了从三维到准二维和从三维到准一维的收敛性和降维率。本文报道了具有铁磁/反铁磁相互作用和一维/二维/三维各种外部电位的bec基态的大量数值结果。

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引用次数: 0

Investigation of new analytical and numerical solutions of the extended (2+1) dimensional Boussinesq equation using fractional derivative approaches 用分数阶导数方法研究扩展（2+1）维Boussinesq方程新的解析解和数值解

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-01-11 DOI: 10.1016/j.jcp.2026.114654

İlknur Kızıl , Ulviye Demirbilek , Ercan Çelik

This study investigates the new fractional (2+1)-dimensional, extended Boussinesq (eBO) equation, which models the behavior of shallow water waves in channels with constant depth and flow velocity. This equation holds considerable relevance in fields such as ocean engineering, coastal hydrodynamics, plasma physics, and nonlinear wave theory. By applying the

(m + 1 / G^{'})

–expansion method, the sub-equation method, and dummyTXdummy– the modified extended tanh function method within the framework of conformable derivatives, a wide array of analytical traveling wave solutions is obtained. These include dark, bright, periodic, singular, exponential, and generalized hyperbolic-type solitons with kink-like features. The fractional transformation technique transforms the original fractional partial differential equations into ordinary differential equations, thereby simplifying the solution process. Moreover, the residual power series method (RPSM) is employed to approximate the solution of this equation, and modulation instability (MI) analysis is conducted to evaluate the stability of the obtained analytical solutions. The study includes comparison tables and various graphical representations to validate the solutions. The numerical findings demonstrate that all methods effectively provide exact and approximate solutions to nonlinear fractional differential equations. The temporal progression and spatial features of the solutions are visualized through 2D, 3D, and contour plots with a comparison of different fractional values. Computational validations are conducted using software, demonstrating the efficiency and general applicability of the proposed approach.

本文研究了新的分数（2+1）维扩展Boussinesq （eBO）方程，该方程模拟了浅水波在恒定深度和恒定流速的通道中的行为。该方程在海洋工程、海岸流体力学、等离子体物理和非线性波浪理论等领域具有相当大的相关性。采用（m+1/G’）展开法、子方程法和dummyTXdummy -改进的扩展tanh函数法，在适形导数的框架下，得到了广泛的行波解析解。这些孤子包括暗孤子、亮孤子、周期孤子、奇异孤子、指数孤子和具有扭结样特征的广义双曲型孤子。分数阶变换技术将原来的分数阶偏微分方程转化为常微分方程，从而简化了求解过程。利用残差幂级数法（RPSM）逼近方程的解，并进行了调制不稳定性分析（MI）来评价所得解析解的稳定性。该研究包括比较表和各种图形表示来验证解决方案。数值结果表明，所有方法都能有效地提供非线性分数阶微分方程的精确近似解。通过2D、3D和等高线图来可视化解决方案的时间进展和空间特征，并对不同分数值进行比较。利用软件进行了计算验证，证明了所提出方法的效率和一般适用性。

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引用次数: 0

BiLO: Bilevel Local Operator Learning for PDE Inverse Problems PDE反问题的双层局部算子学习

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-01-11 DOI: 10.1016/j.jcp.2026.114679

Ray Zirui Zhang , Christopher E. Miles , Xiaohui Xie , John S. Lowengrub

We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with respect to the PDE parameters. At the lower level, we train a neural network to locally approximate the PDE solution operator in the neighborhood of a given set of PDE parameters, which enables an accurate approximation of the descent direction for the upper level optimization problem. The lower level loss function includes the least-square penalty of both the residual and its derivative with respect to the PDE parameters. We apply gradient descent simultaneously on both the upper and lower level optimization problems, leading to an effective and fast algorithm. The method, which we refer to as BiLO (Bilevel Local Operator learning), is also able to efficiently infer unknown functions in the PDEs through the introduction of an auxiliary variable. We provide a theoretical analysis that justifies our approach. Through extensive experiments over multiple PDE systems, we demonstrate that our method enforces strong PDE constraints, is robust to sparse and noisy data, and eliminates the need to balance the residual and the data loss, which is inherent to the soft PDE constraints in many existing methods.

将偏微分方程反问题表述为双层优化问题，提出了一种基于神经网络的求解偏微分方程反问题的新方法。在上层，我们将相对于PDE参数的数据丢失最小化。在较低的层次上，我们训练了一个神经网络来局部逼近PDE解算子在给定PDE参数集的邻域，这使得能够精确地逼近上层优化问题的下降方向。较低水平的损失函数包括残差及其导数相对于PDE参数的最小二乘惩罚。我们将梯度下降同时应用于上层和下层的优化问题，从而得到了一个高效、快速的算法。该方法，我们称之为BiLO（双层局部算子学习），也能够通过引入辅助变量有效地推断pde中的未知函数。我们提供了一个理论分析来证明我们的方法是正确的。通过对多个PDE系统的大量实验，我们证明了我们的方法执行强PDE约束，对稀疏和噪声数据具有鲁棒性，并且消除了许多现有方法中软PDE约束所固有的残差和数据丢失平衡的需要。

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引用次数: 0

A consistent and scalable framework suitable for boiling flows using the conservative diffuse interface method 用保守扩散界面法建立了一个适用于沸腾流动的一致可扩展框架

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-01-11 DOI: 10.1016/j.jcp.2026.114680

Lorenz Weber , Aritra Mukherjee , Andreas G. Class , Luca Brandt

Interface-resolved simulations are essential for predicting and understanding boiling heat transfer phenomena. Such simulations generally come at a high computational cost, which continues to motivate the development of efficient frameworks. In recent years, conservative second-order phase field methods have gained popularity due to their efficient representation of phase interfaces. However, their potential for simulating complex boiling phenomena has not yet been explored. To address this gap, we develop a consistent and highly efficient framework suitable for simulating large-scale boiling flows. We derive a set of mixture equations to describe the two-phase flow. The mixture equations are coupled with the accurate conservative diffuse interface method [1] to capture the interface. We present additional terms in the momentum balance equation and demonstrate that the proposed momentum balance modifications are mandatory for accurately capturing phase-change-induced pressure jumps. To solve the set of equations, an alternative Fast Fourier Transform (FFT)-based pressure solution scheme is proposed. Additionally, a modified kinetic phase change model is utilized that does not involve calculating temperature gradients and avoids problem-dependent parameters. The framework is tested against a variety of benchmark simulations, both with and without phase change. Moreover, we achieve improved accuracy when simulating bubble dynamics without phase change at high density ratios. We show that the proposed FFT-based pressure solution scheme exhibits superior performance in calculating interfacial pressure jumps compared with a commonly used FFT solver. Regardless of phase change, more accurate startup behaviour is observed. In the presence of phase change, we are successful in removing interfacial pressure oscillations. Across all phase-change benchmark simulations, the new phase change model consistently provides reliable results. Finally, we successfully simulate the dynamics of bubbles in superheated liquid subjected to gravity and validate the results with experimental data.

界面解析模拟对于预测和理解沸腾传热现象至关重要。这样的模拟通常需要很高的计算成本，这将继续推动高效框架的开发。近年来，保守二阶相场法因其对相界面的有效表征而受到广泛的关注。然而，它们模拟复杂沸腾现象的潜力尚未得到探索。为了解决这一差距，我们开发了一个适用于模拟大规模沸腾流动的一致且高效的框架。我们推导了一组描述两相流的混合方程。将混合方程与精确保守扩散界面法[1]耦合以捕获界面。我们在动量平衡方程中提出了附加项，并证明了所提出的动量平衡修正对于准确捕获相变引起的压力跳变是必需的。为了求解这组方程，提出了一种基于快速傅立叶变换（FFT）的压力求解方案。此外，采用了一种改进的动力学相变模型，该模型不涉及计算温度梯度，避免了与问题相关的参数。该框架针对各种基准模拟进行了测试，包括有和没有相变。此外，在高密度比下模拟无相变气泡动力学时，我们获得了更高的精度。我们表明，与常用的FFT求解器相比，所提出的基于FFT的压力求解方案在计算界面压力跳变方面表现出优越的性能。无论相位变化如何，都可以观察到更准确的启动行为。在相变存在的情况下，我们成功地消除了界面压力振荡。在所有相变基准模拟中，新的相变模型始终提供可靠的结果。最后，我们成功地模拟了重力作用下过热液体中气泡的动力学，并用实验数据验证了结果。

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引用次数: 0

Enabling probabilistic learning on manifolds through double diffusion maps 通过双扩散映射实现流形的概率学习

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-01-09 DOI: 10.1016/j.jcp.2026.114663

Dimitris G. Giovanis , Nikolaos Evangelou , Ioannis G. Kevrekidis , Roger G. Ghanem

We present a generative learning framework for probabilistic sampling that extends Probabilistic Learning on Manifolds (PLoM), which is designed to generate statistically consistent realizations of a random vector in a finite-dimensional Euclidean space, informed by a (representative) set of observations. In its original form, PLoM constructs a reduced-order probabilistic model by combining three main components: (a) kernel density estimation to approximate the underlying probability measure, (b) Diffusion Maps to characterize the manifold of the data, and (c) a reduced-order Itô Stochastic Differential Equation (ISDE) to sample from the learned distribution. However, its sampling dynamics are posed in the ambient space and the retained number of reduced coordinates is chosen by projection-reconstruction error. In practice, this often (i) requires more coordinates than the data’s intrinsic dimension to achieve stable sampling and (ii) lacks a smooth, basis-independent lifting back to the data domain; moreover, standard Diffusion Maps emphasize harmonic eigenfunctions and can miss non-harmonic latent structure. We address these limitations by decoupling geometry learning from sampling: a first Diffusion Maps pass identifies non-harmonic coordinates on which we formulate a full-order ISDE directly in the latent space, while Double Diffusion Maps captures multiscale geometric features and Geometric Harmonics (GH) learns a smooth lifting map to the ambient variables that is independent of the particular diffusion basis. This hybrid design preserves the system’s dynamical richness with a compact geometric representation and enables principled out-of-sample inference. The effectiveness and robustness of the proposed method are illustrated through two numerical studies: one based on data generated from two-dimensional Hermite polynomial functions and another based on high-fidelity simulations of a detonation wave in a reactive flow.

我们提出了一个概率抽样的生成式学习框架，扩展了流形上的概率学习（PLoM），该框架旨在生成有限维欧几里得空间中随机向量的统计一致实现，由一组（代表性）观察结果提供信息。在其原始形式中，PLoM通过结合三个主要组成部分构建了一个降阶概率模型：(a)核密度估计来近似潜在的概率度量，(b)扩散映射来表征数据的流形，以及(c)一个降阶Itô随机微分方程（ISDE）来从学习分布中采样。然而，它的采样动态是在环境空间中进行的，并通过投影重建误差来选择保留的约简坐标数。在实践中，这通常(i)需要比数据的固有维度更多的坐标来实现稳定的采样，（ii）缺乏平滑的、与基无关的提升回数据域；此外，标准扩散图强调谐波特征函数而忽略非谐波潜在结构。我们通过从采样中解耦几何学习来解决这些限制：第一次扩散地图通过识别非调和坐标，我们直接在潜在空间中制定全阶ISDE，而双扩散地图捕获多尺度几何特征，几何谐波（GH）学习到独立于特定扩散基础的环境变量的平滑提升图。这种混合设计通过紧凑的几何表示保留了系统的动态丰富性，并使原则的样本外推理成为可能。通过两个数值研究证明了该方法的有效性和鲁棒性：一个是基于二维Hermite多项式函数生成的数据，另一个是基于高保真的反应流爆震波模拟。

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引用次数: 0

Toward accurate and efficient multi-moment finite volume method for large eddy simulations of compressible flows on unstructured grids 非结构网格上可压缩流大涡模拟的精确、高效多矩有限体积法

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-01-09 DOI: 10.1016/j.jcp.2026.114668

Ying Yang , Feng Xiao , Bin Xie

A novel multi-moment finite volume method is proposed for the solutions of linear and nonlinear hyperbolic equations on unstructured grids and further investigated for implicit large eddy simulation of compressible turbulence. Different from the previous volume integrated average and point value based multi-moment (VPM) method, the present scheme first reconstructs the solution values and first-order derivatives at boundary surfaces and then constructs a quadratic polynomial over each cell using Gauss divergence theorem. It eliminates the need to directly compute second derivatives of solution variables, which is more efficient than conventional finite volume discretizations at third-order accuracy. The so-called VPM-FR (VPM with face-based reconstruction) formulates novel spatial reconstruction within a compact stencil consisting of only face neighbouring cells, which substantially improves the numerical accuracy, efficiency, robustness as well as algorithmic simplicity. Fourier analysis is also conducted to verify the numerical properties of VPM-FR which are compared against the previous version of VPM scheme. Besides, a new limiting projection approach is devised to use a high-order limiter function which effectively suppresses the numerical oscillation in the vicinity of discontinuities. Numerical results of various benchmark tests are presented for the advection, Euler and Navier-Stokes equations which validate the excellent performance of VPM-FR scheme that well resolves broadband turbulence and the sharp shock profiles with a reduction in computation cost.

提出了求解非结构网格上线性和非线性双曲型方程的一种新的多矩有限体积法，并进一步研究了可压缩湍流的隐式大涡模拟。与以往的体积积分平均和基于点值的多矩（VPM）方法不同，该方法首先在边界面上重建解值和一阶导数，然后利用高斯散度定理在每个单元上构造二次多项式。它消除了直接计算解变量二阶导数的需要，这比传统的三阶精度有限体积离散更有效。所谓的vvm - fr （VPM with face-based reconstruction）在仅由人脸相邻单元组成的紧凑模板内制定了新颖的空间重建，这大大提高了数值精度，效率，鲁棒性以及算法的简单性。通过傅里叶分析验证了VPM- fr格式的数值特性，并与之前版本的VPM格式进行了比较。此外，设计了一种新的极限投影方法，利用高阶极限函数有效地抑制了不连续点附近的数值振荡。对平流方程、Euler方程和Navier-Stokes方程进行了各种基准测试，验证了vvm - fr格式在解决宽带湍流和剧烈激波剖面问题上的优异性能，并降低了计算成本。

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引用次数: 0

An improved lattice Boltzmann method with a novel conservative boundary scheme for viscoelastic fluid flows 粘弹性流体流动的一种新的保守边界格式改进晶格玻尔兹曼方法

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-01-09 DOI: 10.1016/j.jcp.2026.114667

Yuan Yu , Siwei Chen , Yuting Zhou , Lei Wang , Hai-Zhuan Yuan , Shi Shu

The high Weissenberg number problem has been a persistent challenge in the numerical simulation of viscoelastic fluid flows. This paper presents an improved lattice Boltzmann method for solving viscoelastic flow problems at high Weissenberg numbers. The proposed approach employs two independent two-relaxation-time regularized lattice Boltzmann models to solve the hydrodynamic field and conformation tensor field of viscoelastic fluid flows, respectively. The viscoelastic stress computed from the conformation tensor is directly embedded into the hydrodynamic field using a newly proposed local velocity discretization scheme, thereby avoiding spatial gradient calculations. The constitutive equations are treated as convection-diffusion equations and solved using an improved convection-diffusion model specifically designed for this purpose, incorporating a novel auxiliary source term that eliminates the need for spatial and temporal derivative computations. Additionally, a conservative non-equilibrium bounce-back (CNEBB) scheme is proposed for implementing solid wall boundary conditions in the constitutive equations. The robustness of the present algorithm is validated through a series of benchmark problems. The simplified four-roll mill problem demonstrates that the method effectively improves numerical accuracy and stability in bulk regions containing stress singularities. The Poiseuille flow problem validates the accuracy of the current algorithm with the CNEBB boundary scheme at extremely high Weissenberg numbers (tested up to

Wi = 10000

). The flow past a circular cylinder problem confirms the superior stability and applicability of the scheme for complex curved boundary problems compared to other existing common schemes.

高Weissenberg数问题一直是粘弹性流体流动数值模拟中的一个难题。本文提出了求解高维森伯格数粘弹性流动问题的改进晶格玻尔兹曼方法。该方法采用两个独立的双松弛时间正则化晶格玻尔兹曼模型分别求解粘弹性流体流动的水动力场和构象张量场。采用新提出的局部速度离散化方案，将构象张量计算得到的粘弹性应力直接嵌入到流体动力场中，从而避免了空间梯度计算。本构方程被视为对流-扩散方程，并使用专门为此目的设计的改进的对流-扩散模型进行求解，该模型包含了一个新的辅助源项，消除了对空间和时间导数计算的需要。此外，提出了一种保守的非平衡反弹（CNEBB）格式来实现本构方程中的实体壁边界条件。通过一系列的基准问题验证了该算法的鲁棒性。简化后的四辊轧机问题表明，该方法有效地提高了包含应力奇点的块体区域的数值精度和稳定性。泊泽维尔流问题验证了CNEBB边界格式在极高的Weissenberg数（测试Wi=10000）下的当前算法的准确性。经过圆柱的流动问题验证了该格式在复杂曲面边界问题上的稳定性和适用性。

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引用次数: 0

An implicit shock tracking method for simulation of shock-dominated flows over complex domains using mesh-based parametrizations 基于网格参数化的复杂区域激波主导流动模拟的隐式激波跟踪方法

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-01-09 DOI: 10.1016/j.jcp.2025.114647

Alexander M. Pérez Reyes, Matthew J. Zahr

A mesh-based parametrization is a parametrization of a geometric object that is defined solely from a mesh of the object, e.g., without an analytical expression or computer-aided design (CAD) representation of the object. In this work, we propose a mesh-based parametrization of an arbitrary d′-dimensional object embedded in a d-dimensional space using tools from high-order finite elements. Using mesh-based parametrizations, we construct a boundary-preserving parametrization of the nodal coordinates of a computational mesh that ensures all nodes remain on all their original boundaries. These boundary-preseving parametrizations allow the nodes of the mesh to move only in ways that will not change the computational domain. They also ensure nodes will not move between boundaries, which would cause issues assigning boundary conditions for partial differential equation simulations and lead to inaccurate geometry representations for non-smooth boundary transitions. Finally, we integrate boundary-preserving, mesh-based parametrizations into high-order implicit shock tracking, an optimization-based discontinuous Galerkin method that moves nodes to align mesh faces with non-smooth flow features to represent them perfectly with inter-element jumps, leaving the intra-element polynomial basis to represent smooth regions of the flow with high-order accuracy. Mesh-based parametrizations enable implicit shock tracking simulations of shock-dominated flows over geometries without simple analytical parametrizations. Several demonstrations of mesh-based parametrizations are provided to: (1) give concrete examples of the formulation, (2) show that accurate parametrizations can be obtained despite the surrogate surfaces only being C⁰, (3) show they integrate seemlessly with implicit shock tracking and can be used to parametrize surfaces without explicit expressions, and (4) effectively parametrize complex geometries and prevent nodes from moving off their original boundaries.

基于网格的参数化是一种几何对象的参数化，它仅从对象的网格中定义，例如，不使用对象的解析表达式或计算机辅助设计（CAD）表示。在这项工作中，我们提出了一种基于网格的参数化方法，该方法使用高阶有限元工具对嵌入在d维空间中的任意d维对象进行参数化。使用基于网格的参数化，我们构建了计算网格的节点坐标的边界保持参数化，以确保所有节点保持在所有原始边界上。这些保持边界的参数化允许网格节点仅以不会改变计算域的方式移动。它们还确保节点不会在边界之间移动，这将导致为偏微分方程模拟分配边界条件的问题，并导致非光滑边界转换的不准确几何表示。最后，我们将基于边界保持的网格参数化集成到高阶隐式激波跟踪中，这是一种基于优化的不连续伽辽金方法，该方法移动节点使网格面与非光滑流动特征对齐，以单元间跳跃完美地表示它们，留下单元内多项式基以高阶精度表示流动的光滑区域。基于网格的参数化可以在没有简单分析参数化的情况下对几何形状的激波主导流动进行隐式激波跟踪模拟。提供了几个基于网格的参数化的演示：(1)给出了公式的具体示例；(2)表明，尽管代理曲面只有C0，但可以获得准确的参数化；(3)表明它们与隐式冲击跟踪无缝集成，可以用于参数化曲面，而不需要显式表达式；(4)有效地参数化复杂几何形状并防止节点偏离其原始边界。

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引用次数: 0

A dual physics-informed neural network for topology optimization 拓扑优化的双物理信息神经网络

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-01-08 DOI: 10.1016/j.jcp.2026.114666

Ajendra Singh , Souvik Chakraborty , Rajib Chowdhury

We propose a novel dual physics-informed neural network for topology optimization (DPNN-TO), which merges physics-informed neural networks (PINNs) with the traditional SIMP-based topology optimization (TO) algorithm. This approach leverages two interlinked neural networks–a displacement network and an implicit density network-connected through an energy-minimization-based loss function derived from the variational principles of the governing equations. By embedding deep learning within the physical constraints of the problem, DPNN-TO eliminates the need for large-scale data and analytical sensitivity analysis, addressing key limitations of traditional methods. The framework efficiently minimizes compliance through energy-based objectives while enforcing volume fraction constraints, producing high-resolution designs for both 2D and 3D optimization problems. Extensive numerical validation demonstrates that DPNN-TO outperforms conventional methods, solving complex structural optimization scenarios with greater flexibility and computational efficiency, while addressing challenges such as multiple load cases and three-dimensional problems without compromising accuracy.

本文提出了一种新的双物理通知神经网络拓扑优化（DPNN-TO），它将物理通知神经网络（pinn）与传统的基于simp的拓扑优化（TO）算法相结合。这种方法利用了两个相互连接的神经网络——位移网络和隐式密度网络，它们通过由控制方程的变分原理导出的基于能量最小化的损失函数连接起来。通过将深度学习嵌入到问题的物理约束中，DPNN-TO消除了对大规模数据和分析灵敏度分析的需求，解决了传统方法的关键局限性。该框架通过基于能量的目标有效地减少了合规性，同时实施了体积分数限制，为2D和3D优化问题提供了高分辨率设计。大量的数值验证表明，DPNN-TO优于传统方法，以更大的灵活性和计算效率解决复杂的结构优化方案，同时在不影响精度的情况下解决多种载荷情况和三维问题等挑战。

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引用次数: 0