International Journal for Numerical Methods in Fluids最新文献

Following the proposition of the original AWENO (Alternative Formulation of Weighted Essentially Non-Oscillatory) FD (Finite Difference) scheme, we construct the new AMDCD FD scheme, an Alternative formulation of the linear FD scheme with Minimized Dispersion and Controllable Dissipation, in this article. Spectral analysis shows that the proposed AMDCD FD scheme can be more efficient in resolving smooth solutions due to the flexibility in controlling dissipation. To efficiently solve compressible flows with discontinuities, we further combined the proposed AMDCD FD scheme with the original AWENO FD scheme using a hybrid interpolation scheme, in which the optimized linear MDCD (Minimized Dispersion and Controllable Dissipation) interpolation scheme would be switched to the nonlinear WENO (Weighted Essentially Non-Oscillatory) type interpolation scheme gradually as the flow structures are in transition from smooth region towards the vicinity of discontinuities. Therefore, the resulting hybrid AWENO-AMDCD FD scheme is suitable for solving compressible flows with broad-scale flow structures and/or shock waves. A series of one-, two-, and three-dimensional compressible flow problems are numerically tested to demonstrate the accuracy, superior resolution, as well as the robustness of the proposed hybrid AWENO-AMDCD FD scheme.

Physics-informed neural network (PINN) has become a potential technology for fluid dynamics simulations, but traditional PINN has low accuracy in simulating incompressible flows, and these problems can lead to PINN not converging. This paper proposes a physics-informed neural network method (KA-PINN) based on the Kolmogorov–Arnold Neural (KAN) network structure. It is used to solve two-dimensional and three-dimensional incompressible fluid dynamics problems. The flow field is reconstructed and predicted for the two-dimensional Kovasznay flow and the three-dimensional Beltrami flow. The results show that the prediction accuracy of KA-PINN is improved by about 5 times in two dimensions and 2 times in three dimensions compared with the fully connected network structure of PINN. Meanwhile, the number of network parameters is reduced by 8 to 10 times. The research results not only verify the application potential of KA-PINN in fluid dynamics simulations, but also demonstrate the feasibility of KAN network structure in improving the ability of PINN to solve and predict flow fields. This study can reduce the dependence on traditional numerical methods for solving fluid dynamics problems.

We present an augmented Lagrangian trust-region method to efficiently solve constrained optimization problems governed by large-scale nonlinear systems with application to partial differential equation-constrained optimization. At each major augmented Lagrangian iteration, the expensive optimization subproblem involving the full nonlinear system is replaced by an empirical quadrature-based hyperreduced model constructed on-the-fly. To ensure convergence of these inexact augmented Lagrangian subproblems, we develop a bound-constrained trust-region method that allows for inexact gradient evaluations, and specialize it to our specific setting that leverages hyperreduced models. This approach circumvents a traditional training phase because the models are built on-the-fly in accordance with the requirements of the trust-region convergence theory. Two numerical experiments (constrained aerodynamic shape design) demonstrate the convergence and efficiency of the proposed work. A speedup of $��12�.�7�\times �$ (for all computational costs, even costs traditionally considered “offline” such as snapshot collection and data compression) relative to a standard optimization approach that does not leverage model reduction is shown.

This article develops a high-order finite element scheme in an approximate solution of the two-dimensional Rayleigh–Stokes problem for a heated generalized second-grade fluid with fractional derivatives. The constructed approach consists of approximating the exact solution by interpolation in time while the finite element technique is used in the approximation of the spatial derivatives. This combination is simple and easy to implement. The stability and error estimates of the developed strategy are deeply analyzed in the $��{�L�}^{�\infty �}�$-norm. The theoretical studies suggest that the proposed method is unconditionally stable, convergent with order $��O�(�{�\sigma �}^{�1�+�\gamma �}�+�{�h�}^{�p�}�)�$, faster, and more efficient than a broad range of numerical schemes discussed in the literature for the considered time fractional partial differential equation. Some numerical examples are carried out to show the applicability and viability of the new algorithm.

In coastal and offshore engineering, the intense water–soil motion poses significant challenges to the safety of buildings and structures. The smoothed particle hydrodynamics (SPH) method, as a mesh-free Lagrangian solver, has considerable advantages in the numerical resolution of such problems. SPH models for the water–soil two-phase flow can be categorized into the multilayer type and the single-layer type. Although the single-layer model envisions a simpler algorithm and higher computational efficiency, its accuracy, stability, and recovery of interfacial details are far from satisfactory. In the present work, an improved single-layer model is established to alleviate these limitations. First, the soakage function, which takes effect near the phase interface, is introduced to characterize the two-phase coupling status. Additionally, the stress diffusion term and a modified density diffusion term applicable in density discontinuity scenario are introduced to ease the numerical oscillation. Finally, to remove the unphysical voids in the interfacial region, the particle shifting technique with special treatment tailored for free-surface particles is implemented. Validations of the proposed model are carried out by a number of numerical tests, including the erodible dam-break problem, the wall-jet scouring, the flushing case, and the water jet excavation. Appealing agreements with either experimental data or published numerical results have been achieved, which verifies the accuracy, stability, and robustness of the proposed model for water–soil two-phase flows.

The classical WENO schemes perform well for most flow field simulations, they may encounter the ‘Cannikin Law’ trap, that is, the lowest accuracy order of the scheme may have a significant influence on the simulation. In this article, a novel WENO scheme (termed HPWENO) with improved convergence order is proposed to alleviate this issue. The research in this article is structured around three key steps: Firstly, the stencil is classified as either smooth stencil or non-smooth stencil by using the classification strategy of the hybrid WENO scheme. Secondly, perturbed polynomial reconstruction with double free-parameters is proposed. Finally, the new reconstruction coefficients containing multiple free-parameters, built on the classical fifth-order WENO schemes, are obtained by using the perturbed polynomial reconstruction. Compared to the fifth-order WENO schemes, a maximum two-order of accuracy improvement in candidate stencils and one-order of accuracy improvement in global stencil can be achieved by adaptively adjusting the values of these free-parameters, resulting in sixth-order accuracy in global stencil and fifth-order accuracy in candidate stencils. Compared to the classical fifth-order WENO5-Z scheme and the WENO-AO(5,3) scheme, numerical examples show that the HPWENO schemes have higher convergence ratio, provide sharper solution profiles near discontinuities, and perform well in resolving small-scale structures. Compared to the sixth-order WENO-CU6 scheme and the seventh-order WENO7-Z scheme, the proposed HPWENO schemes outperform the two schemes in resolving the small-scale vortex of two-dimensional issues, and it saves approximately 15% and 25% of computational resources, respectively.

We introduce a new hybrid numerical approach that integrates the Mimetic Finite Difference (MFD) and Discontinuous Galerkin (DG) methods, termed the MFD-DG method. This technique leverages the MFD method to adeptly manage arbitrary quadrilateral meshes and full permeability tensors, addressing the flow equation for both edge-center and cell-center pressures. It also provides an approximation for phase fluxes across interfaces and within cells. Subsequently, the DG scheme, equipped with a slope limiter, is applied to the convection-dominated transport equation to compute nodal and cell-average water saturations. We present two numerical examples that demonstrate the MFD's capability to deliver high-precision approximations of pressure and flux distributions across a broad spectrum of grid types. Furthermore, our proposed hybrid MFD-DG method demonstrates a significantly enhanced ability to capture sharp water flooding fronts with greater accuracy compared to the traditional Finite Difference (FD) Method. To further demonstrate the efficacy of our approach, four numerical examples are provided to illustrate the MFD-DG method's superiority over the classical Finite Volume (FV) method and MFDM, particularly in scenarios characterized by anisotropic permeability tensors and intricate geometries.