International Journal of Computational Methods

Appropriate mesh refinement plays a vital role in the accuracy and convergence of computational fluid dynamics solvers. This work is an extension of the previous work that further demonstrates the accuracy of the 3D adaptive mesh refinement method by comparing the accuracy measures between the ones derived from the analytical fields and those identified by the refined meshes. The adaptive mesh refinement method presented in this study is based on the law of mass conservation for three-dimensional incompressible or compressible steady fluid flows. The assessment of the performance of the adaptive mesh refinement method considers its key features such as drawing closed streamline and identification of singular points, asymptotic planes, and vortex axis. Several illustrative examples of the applications of the 3D mesh refinement method with a multi-level refinement confirm the accuracy and efficiency of the proposed method. Furthermore, the results demonstrate that the adaptive mesh refinement method can provide accurate and reliable qualitative measures of 3D computational fluid dynamics problems.

In this paper, a new method named Improved Finite Integration Method (IFIM) is proposed for solving Time Fractional Diffusion Equations (TFDEs). In the IFIM, the Extended Simpson’s Rule (ESR) is employed for numerical quadrature in spatial discretization. Besides, the Piecewise Quadratic Interpolation (PQI) in sense of the Hadamard finite-part integral is utilized for time discretization. Compared with the primary Finite Integration Method (FIM) with Trapezoidal rule which uses the finite difference scheme to address the time discretization, the combination of ESR and PQI in IFIM will lead to a better performance in solving TFDEs. Numerical examples are performed and compared to show the superiority of IFIM. It can also be found that the IFIM is able to obtain a higher accuracy without losing the stability and efficiency.

In this paper, a physics-informed recurrent neural network (PIRNN) is proposed to solve time-dependent partial differential equations (PDEs), which devices LSTM cells to ensure the continuity of field variables in time stepping. The number of the training parameters is sharply reduced due to the parameter sharing implemented in LSTM cells so that the efficiency of PIRNN greatly improves. In order to preferably simulate the physical process and improve the accuracy of prediction, the predicted values of the current layer are employed as the input of the next layer, which exploits the idea of FDM. Thus, more information can be applied for the next prediction, and the field values at different time steps can be obtained as well. Besides, the loss value of the governing equation, the loss value of the initial condition and the loss value of the boundary condition are used to construct the loss function so that the physical law is also fully utilized. Finally, we conduct the heat conduction equation, wave equation and 2D Burgers equation to demonstrate the performance of PIRNN. Numerical experiments show that the proposed PIRNN can accurately and efficiently predict the field values at any time, in which nonuniform time steps can be used and the error accumulation is avoided.

This paper presents the modified boundary knot method (MBKM) for solving the homogeneous harmonic type boundary value problems (BVPs). Since no non-singular general solutions are applicable for harmonic-type equations, the general solutions of Helmholtz-type operator with a free parameter $\lambda$ can be used to approximate the solutions of these problems by adjusting the $\lambda$. Compared with the classical boundary knot method (BKM) where the source nodes are the same as the boundary collocation nodes, the MBKM employs the ghost points method, which resets the source points to a disk-like region covering the primary problem area. This modification results in better accuracy without any increase in the computational cost. On the other hand, as the accuracy of the MBKM depends heavily on the parameter $\lambda$, the effective condition number (ECN) is first employed to find a proper $\lambda$ in MBKM. Several 2D and 3D numerical examples are listed to illustrate the superior performance of the MBKM in solving harmonic-type BVPs. The accuracy of MBKM is improved by one to two orders of magnitude compared to the classical BKM. Meanwhile, the validity of the ECN for obtaining a suitable $\lambda$ for problems under complex geometric regions is also demonstrated.

In this paper, the explicit solving of pressure Poisson equation and GPU parallelization were employed to improve the efficiency of MPS method, which is one of the mainstream particle methods. The performance of the explicit GPU parallel MPS method is discussed using two-dimensional dam-break and sloshing problems. The reliability and accuracy of the developed algorithm were validated against the results of traditional implicit solving method (based on GMRES) and experiment. In terms of efficiency improvement, compared with the traditional CPU-based serial solver, the explicit GPU-parallelized algorithm greatly reduces the computational time of the pressure Poisson equation. More specifically, the maximum acceleration ratios of 11.486 and 13.89 can be obtained by numerical simulation for 2D dam-break and sloshing problems with different particle numbers.

The current three-dimensional averaging mathematical model of flow, also known as the Reynolds averaged Navier–Stokes equations or Reynolds equations, was developed based on the idea of Reynolds in 1895. This model is given by the classical averaging of velocity and pressure parameters from the three-dimensional Navier–Stokes equations. However, by doing this, these averaging parameters obtained by this classical approach are not generalized in comparison to ones estimated by the dual approach. This paper proposes a dual approach to establishing the three-dimensional flow equation. The model setup is more complicated than the classical model in terms of integration because the procedure can be repeated several times. In this paper, the authors perform twice: (1) first, integration of the velocity and pressure parameters from time $t$ to $t+T_m$, with time $T_m<T$, where $T$ is the repeated period of parameters; (2) second, integration from time t to $t+T$. Fluctuating quantities such as velocity and pressure in turbulent flow, over time, are simulated using trigonometric Fourier series. The three-dimensional flow model obtained from this dual approach could provide more accurate results than those given by the Reynolds averaged Navier–Stokes equations.

Topology optimization (TO) can generate innovative conceptual configurations with shell–infill geometric features by distributing materials optimally within the design domain. However, physics-based topology optimization methods require repeated finite element analysis and variable updating, in which expensive computational cost limits their applications in wider industrial fields, especially for topology optimization for shell–infill structures. Fortunately, the arising of the data-based topology optimization method using deep learning has paved the way to realize real-time topology prediction for shell–infill structures. In this work, a novel and differentiable structural similarity (SSIM) loss function is introduced into the conditional generative adversarial network (cGAN) to construct the SSIM-cGAN model, and the single-channel coding strategy of initial condition is proposed to simplify the inputs of the deep learning model. SSIM-cGAN can generate shell–infill structures in real time after training with a small-scale dataset. The results generated by SSIM-cGAN and cGAN were put together for comparison, demonstrating that the shell–infill structure generated by SSIM-cGAN has lower error than cGAN, and the shell layer and porous infill structures are more integrated.

For the purpose of a better understanding of the mechanical behavior of pipe joints’ interface which is critical for the integral performance of a pipe system, and excessive torsional loading that is typical for their interfacial failure, the interfacial behavior of adhesive bonded pipe joints under torsion loads is theoretically studied throughout the full-ranged failure process based on a local bond-slip law with hardening and exponential softening. Firstly, closed-form solutions for the interfacial shear stress distribution and load–displacement response are derived to describe the four basic loading stages. Secondly, a simplified law is used by changing the exponential softening law into a tri-linear one to make the comparison. According to the analytical solutions of two laws, the influences of the bond length on load–displacement curve including the ultimate loads and relative slips are discussed, with the similarities and differences between the two laws being studied. Thirdly, by introducing a dimensionless damage parameter, the results of the finite element method (FEM) using ABAQUS modeling are compared with analytical results. Based on these coincident results, the parametric studies of bond lengths and ratios of torsion stiffness on specific cases were conducted to explain the stress transfer mechanism and interface crack propagation. Both their ultimate bearing capacity and ductility improve in an increase of bond lengths, while the ductility reduces as the ratio of torsion stiffness increases. The outcomes of this paper are helpful to improve the safety and applicability of bonded pipe joints in engineering design and application.

Scattering problems have wide applications in the medical and military fields. In this paper, the weighted least-squares (WLS) collocation method based on radial basis functions (RBFs) is developed to solve elastic wave scattering problems, which are governed by the Navier equation and the Helmholtz equations with coupled boundary conditions. The perfectly matched layer (PML) technique is used to truncate the unbounded domain into a bounded domain. The WLS method is constructed by setting the collocation points denser than the trial centers and imposing different weights on different types of boundary conditions. The WLS method can overcome the matrix singularity problem encountered in the Kansa method, and the convergence rate of WLS is $m-2$ for Sobolev kernel with kernel smoothness $m$. Furthermore, compared with the finite element method (FEM) and the Kansa method, WLS can provide higher accuracy and more stable solutions for relatively large angular frequencies. The numerical example with a circular obstacle is used to verify the effectiveness and convergence behavior of the WLS. Besides, the proposed scheme can easily handle irregular obstacles and obtain stable results with high accuracy, which is validated through experiments with ellipse and kite-shaped obstacles.

This study commences with the application of an efficient artificial neural network (ANN)-balancing composite motion optimization (BCMO) approach for finding the optimal material distribution of bi-directional functional graded nanocomposite (FGN) thin plates considering geometrically nonlinear behaviors. To this regard, an ANN-based surrogate model of the high-fidelity isogeometric analysis (IGA) of the geometrically nonlinear Kirchhoff–Love plates based on the Von Kármán nonlinearity theory is first constructed and then employed to predict the values of objectives and constraints required in the BCMO framework. The multi-mesh design approach is utilized to form two separate nonuniform rational B-spline meshes for optimal material distribution and analysis meshes. The unknown control point values of the design mesh are herein selected as the continuous design variables. This allows a possibility to fully explore the complex distribution of optimal material profiles without requiring a significant number of variables. Selected numerical examples with different plate geometries and loading conditions are presented to illustrate the merit features of the proposed approach. Obtained results reveal not only its high accuracy and significant efficiency compared with the conventional approach coupling the BCMO with IGA direct analysis but also the stable ability of the BCMO in finding global optimum material distributions in comparison with two commonly used metaheuristics algorithms, i.e., particle swarm optimization and genetic algorithm.