International Journal for Numerical Methods in Fluids最新文献

We develop a novel Moving Particle Simulation (MPS) method to reproduce the motion of fibers floating in sheared liquids accurately. In conventional MPS schemes, if a fiber suspended in a liquid is represented by a one-dimensional array of MPS particles, it is entirely aligned to the flow direction due to the lack of shear stress difference between fiber–liquid interfaces. To address this problem, we employ the micropolar fluid model to introduce rotational degrees of freedom into the MPS particles. The translational motion of liquid and solid particles and the rotation of solid particles are calculated with the explicit MPS algorithm. The fiber is modeled as an array of micropolar fluid particles bonded with stretching, bending and torsional potentials. The motion of a single rigid fiber is simulated in a three-dimensional shear flow generated between two moving solid walls. We show that the proposed method is capable of reproducing the fiber motion predicted by Jeffery's theory which is different from the conventional MPS simulations.

Deep learning-based methods for solving partial differential equations have become a research hotspot. The approach builds on the previous work of applying deep learning methods to partial differential equations, which avoid the need for meshing and linearization. However, deep learning-based methods face difficulties in effectively solving complex turbulent systems without using labeled data. Moreover, issues such as failure to converge and unstable solution are frequently encountered. In light of this objective, this paper presents an approximation-correction model designed for solving the seepage equation featuring unsteady boundaries. The model consists of two neural networks. The first network acts as an asymptotic block, estimating the progression of the solution based on its asymptotic form. The second network serves to fine-tune any errors identified in the asymptotic block. The solution to the unsteady boundary problem is achieved by superimposing these progressive blocks. In numerical experiments, both a constant flow scenario and a three-stage flow scenario in reservoir exploitation are considered. The obtained results show the method's effectiveness when compared to numerical solutions. Furthermore, the error analysis reveals that this method exhibits superior solution accuracy compared to other baseline methods.

With a view to simulating the entire process of a landslide-triggered tsunami, ranging from tsunami generation to offshore wave propagation, with relatively low computational costs, we present a 2D–3D coupling strategy to bridge 3D MPM–FEM hybrid and 2D shallow water (SW) simulations. Specifically, considering the difference in basis functions between the 3D and 2D analysis methods, we devise a novel variable passing scheme in the domain overlapping method, in which a slightly overlapped domain enables the generated wave to pass through the connection boundaries with as little discrepancy as possible. For the tsunami generation stage in the 3D domain, the hybrid method combining the finite element method (FEM) and material point method (MPM) is adopted. In this method, the 3D governing equation of the solid phase is solved with the MPM, whereas the well-established 3D stabilized FEM is applied to that of the fluid phase in an Eulerian frame. Additionally, the phase-field method is employed to track the free surface of the 3D fluid domain. On the other hand, the SW equation that represents the offshore wave motion in the 2D domain is solved by the 2D stabilized FEM. Several numerical examples are presented to demonstrate the effectiveness of the developed scheme in properly passing the data from 3D/2D to 2D/3D domains.

An accurate numerical tool is presented in this work to investigate the stationary incompressible Navier–Stokes equations. The proposed approach is based on a pseudo-spectral method for discretizing the differential equations and the asymptotic numerical method to convert nonlinear systems into linear algebraic equations. The coupling of the spectral method with the asymptotic numerical method is considered as an efficient algorithm to solve any nonlinear differential equations. Their efficiency and robustness are examined here on the flow fluid in different canal with different geometries. These computational efficiency and performance have been analysed via several numerical and benchmark examples of incompressible fluid flow in lid-driven cavity and vortex shedding over L-Shaped cavity and fluid flow around a square obstacle. The validation of the proposed approach is made by comparison between the obtained results and those calculated using a finite element method or Ansys commercial code. This validation asserts that the presented numerical tool can be promise for solving fluid flow problems with high accuracy.

A novel p-adaptive discontinuous Galerkin (DG) method has been developed to solve the Euler equations on three-dimensional tetrahedral grids. Hierarchical orthogonal basis functions are adopted for the DG spatial discretization while a third order TVD Runge-Kutta method is used for the time integration. A vertex-based limiter is applied to the numerical solution in order to eliminate oscillations in the high order method. An error indicator constructed from the solution of order $���\left(�p�\right)��$ and $���\left(��p�-�1��\right)��$ is used to adapt degrees of freedom in each computational element, which remarkably reduces the computational cost while still maintaining an accurate solution. The developed method is implemented with under the Charm++ parallel computing framework. Charm++ is a parallel computing framework that includes various load-balancing strategies. Implementing the numerical solver under Charm++ system provides us with access to a suite of dynamic load balancing strategies. This can be efficiently used to alleviate the load imbalances created by p-adaptation. A number of numerical experiments are performed to demonstrate both the numerical accuracy and parallel performance of the developed p-adaptive DG method. It is observed that the unbalanced load distribution caused by the parallel p-adaptive DG method can be alleviated by the dynamic load balancing from Charm++ system. Due to this, high performance gain can be achieved. For the testcases studied in the current work, the parallel performance gain ranged from 1.5× to 3.7×. Therefore, the developed p-adaptive DG method can significantly reduce the total simulation time in comparison to the standard DG method without p-adaptation.

The Levenberg–Marquardt algorithm with back-propagated neural network (BLM-NN) based on machine learning is used in a dynamic fashion in this study to examine the 2D boundary layer flow of a nanofluid comprising gyrotactic microorganisms flowing across a stretchable vertically inclined surface (NGM-ISSFM), immersed in a porous medium. An extensively verified finite-element method (FEM) is used to produce the reference data set for BLM-NN by altering five crucial parameters of the flow model in MATLAB. The main objective of this innovative approach is to minimize longer execution times (for larger number of elements) and more expensive digital computer requirements that are the key barriers to opting the FEM, and in order to obtain the entire function instead of the discrete solution that other numerical methods typically produce. To estimate the NGM-ISSFM model's result for diverse scenario, BLM-NN is trained, tested, and validated. Several BLM-NN implementations using MSE-based indices have shown the performance's veracity and validity through descriptive statistics. The results show that when the Prandtl number increases, the temperature profile and density profile of microorganisms fall dramatically, implying that a fluid with a low Prandtl number is required to enhance the rate of heat transmission.

In this work, we present a two-dimensional multimaterial arbitrary Lagrangian–Eulerian (ALE) method for simulating compressible flows in which a novel coupled volume of fluid and level set interface reconstruction (VOSET) method is developed for interface capturing. The VOSET method combines the merits of both the volume of fluid method and the level set method by using a geometrical iterative operation. Compared to the original VOSET method, the novel VOSET method proposed in this work further improves the accuracy and fidelity in interface reconstruction procedure, especially in under-resolved regions. Several typical two-dimensional numerical experiments are presented to investigate the effectiveness of the proposed VOSET method and its performance when coupling with the multimaterial ALE solver. Numerical results demonstrate its good capability in capturing material interfaces during the simulation of compressible two-material flows.

We propose a high-order curvilinear Lagrangian finite element method for shallow water hydrodynamics. This method falls into the high-order Lagrangian framework using curvilinear finite elements. We discretize the position and velocity in continuous finite element spaces. The high-order finite element basis functions are defined on curvilinear meshes and can be obtained through a high-order parametric mapping from a reference element. Considering the variational formulation of momentum conservation, the global mass matrix is independent of time due to the use of moving finite element basis functions. The mass conservation is discretized in a pointwise manner which is referred to as strong mass conservation. A tensor artificial viscosity is introduced to deal with shocks, meanwhile preserving the symmetry property of solutions for symmetric flows. The generic explicit Runge–Kutta method could be adopted to achieve high-order time integration. Several numerical experiments verify the high-order accuracy and demonstrate good performances of using high-order curvilinear elements.