International Journal for Numerical Methods in Fluids最新文献

This article presents a sharp immersed method for simulating electrohydrodynamic (EHD) flows that involve charge evaporation. This well-known multi-scale, multi-physics problem is widely used in various fields, including industry and medicine. The method adopts a fully sharp model, where surface tension and Maxwell stress are treated as surface forces and free charges are concentrated on the zero thickness liquid-vacuum interface. Incorporating charge evaporation imposes strict restrictions on the time-step, as the rate of evaporation sharply increases with surface evolution. To overcome this challenge, an iterative algorithm that couples the electric field and surface charge density is proposed to obtain accurate results, even with significantly large time-steps. To mitigate the numerical residuals near the interface, which may introduce parasitic flows and cause numerical instability, an immersed interface method-based iterative projection method for the Navier–Stokes equations is proposed, in which a traction boundary condition involving multiple surface forces is imposed on the sharp interface. Numerical experiments were carried out, and the results show that the method is splitting-error-free and stable. The sharp immersed method is applied to simulate the electric-induced deformation of an ionic liquid drop with charge evaporation. The results indicate that charge evaporation can suppress the sharp development of Taylor cones at the ends of the drops. These findings have significant implications for the design and optimization of EHD systems in various applications.

Although the gas kinetic schemes (GKS) have emerged as one of the powerful tools for simulating compressible flows, they exhibit several shortcomings. Since the local solution of continuous Boltzmann equation with the Maxwellian distribution function is used to calculate the numerical fluxes at the cell interface, the flux expression in GKS is usually more complicated. In this paper, a high-order simplified gas kinetic flux solver (GKFS) is presented for simulating two-dimensional compressible flows. Circular function-based GKFS (C-GKFS), which simplifies the Maxwellian distribution function into the circular function, combined with an improved weighted essentially non-oscillatory (WENO-Z) scheme is applied to capture more details of the flow fields with fewer grids. As a result, a simple high-order accurate C-GKFS is obtained, which improves the computing efficiency and reduce its complexity to facilitate the practical application of engineering. A series of benchmark-test problems are simulated and good agreement can be obtained compared with the references, which demonstrate that the high-order C-GKFS can achieve the desired accuracy.

This paper presents a high-order Fourier-expansion based differential quadrature method with isothermal and thermal lattice Boltzmann flux solvers (LBFS-FDQ and TLBFS-FDQ) for simulating incompressible flows. The numerical solution in the present method is approximated via trigonometric basis. Therefore, both periodic and non-periodic boundary conditions can be handled straightforwardly without the special treatments as required by polynomial-based differential quadrature methods. The incorporation of LBFS/TLBFS enables the present methods to efficiently simulated various types of flow problems on considerably coarse grids with spectral accuracy. The high-order accuracy, efficiency and competitiveness of the proposed method are comprehensively demonstrated through a wide selection of isothermal and thermal flow benchmarks.

Researchers can incorporate uncertainties in computational fluid dynamics (CFD) that go beyond the inaccuracies caused by numerical discretization thanks to stochastic simulations. This study confirms the validity of current stochastic modeling tools by providing examples of stochastic simulations in conjunction with numerical solutions for incompressible flows. A numerical technique for solving deterministic and stochastic models is developed in this work. Our approach employs the Euler-Maruyama method for stochastic modeling, representing a stochastic version of the third-order explicit-implicit scheme. For the deterministic model, the scheme is third-order accurate. The consistency and stability of the constructed scheme are provided in the mean square sense. The scheme is the predictor–corrector type that is built on two time levels. Moreover, a mathematical model of the Casson nanofluid flow with variable thermal conductivity is given with the effect of the chemical reaction. The appropriate transformations are used to condense the set of partial differential equations (PDEs) down to one that is dimensionless. The scheme is applied for the deterministic and stochastic models of dimensionless flow problems. The velocity profile's deterministic and stochastic behavior are shown using contour plots. Results show that growing values of the thermal mixed convection parameter enhance the velocity profile. This article presents the progress made in stochastic computational fluid dynamics (SCFD) and highlights the energy-related aspects of our discoveries. Our computational approach and stochastic modeling techniques provide new insights into the energy properties of Casson nanofluid flow, specifically regarding the variability of thermal conductivity and chemical processes. Our objective is to clarify the complex interaction of these factors on energy dynamics. This article presents a contemporary summary of the latest SCFD advancements. Additionally, it highlights potential directions for future research and unresolved issues that require attention from the members of the field of computational mathematics.

In this paper, the Allen-Cahn-Multiphase lattice Boltzmann flux solver (AC-MLBFS) is proposed as a new and effective numerical simulation method for multiphase flows with high density ratios. The MLBFS resolves the macroscopic governing equations with the finite volume method and reconstructs numerical fluxes on the cell interface from local solutions to the lattice Boltzmann equation, which combines the advantages of conventional Navier–Stokes solvers and lattice Boltzmann methods for simulating incompressible multiphase flows while alleviating their limitations. Previous MLBFS-based multiphase solvers performed poorly in mass conservation, which might be caused by the excessive numerical diffusion in the Cahn-Hilliard (CH) model used as the interface tracking algorithm. To resolve this problem, the present method proposes using the conservative Allen-Cahn (AC) model as the interfacial tracking algorithm, which can ease the numerical implementation by removing high order derivative terms and alleviate mass leakage by enforcing local mass conservation in the physical model. Numerical validations will be carried out through benchmark tests at high density ratios and in extreme conditions with large Reynolds or Weber numbers. Through these examples, the accuracy and robustness as well as the mass conservation characteristics of the proposed method are demonstrated.

This work presents details and assesses implicit and adaptive mesh-free CFD modelling approaches, to alleviate laborious mesh generation in modern CFD processes. A weighted-least-squares-based, mesh-free, discretisation scheme was first derived for the compressible RANS equations, and the implicit dual-time stepping was adopted for improved stability and convergence. A novel weight balancing concept was introduced to improve the mesh-free modelling on highly irregular point clouds. Automatic point cloud generations based on strand and level-set points were also discussed. A novel, polar selection approach, was also introduced to establish high-quality point collocations. The spatial accuracy and convergence properties were validated using 2D and 3D benchmark cases. The impact of irregular point clouds and various point collocation search methods were evaluated in detail. The proposed weight balancing and the polar selection approaches were found capable of improving the mesh-free modelling on highly irregular point clouds. The mesh-free flexibility was then exploited for adaptive modelling. Various adaptation strategies were assessed using simulations of an isentropic vortex, combining different point refinement mechanisms and collocation search methods. The mesh-free modelling was then successfully applied to transonic aerofoil simulations with automated point generation. A weighted pressure gradient metric prioritising high gradient regions with large point sizes was introduced to drive the adaptation. The mesh-free adaptation was found to effectively improve the shock resolution. The results highlight the potential of mesh-free methods in alleviating the meshing bottleneck in modern CFD.

The Kolmogorov–Petrovsky–Piskunov (KPP) partial differential equation (PDE) is solved in this article using the moving mesh finite difference technique (MMFDM) in conjunction with physics-informed neural networks (PINNs). We construct a time-dependent mesh to obtain approximate solutions for the KPP problem. The temporal derivative is discretized using a backward Euler, while the spatial derivatives are discretized using a central implicit difference scheme. Depending on the error measure, several moving mesh partial differential equations (MMPDEs) are employed along the arc-length and curvature mesh density functions (MDF). The proposed strategy has been suggested to yield remarkably precise and consistent results. To find the approximate solution, we additionally employ physics-informed neural networks (PINNs) to compare the outcomes of the adaptive moving mesh approach. It has been observed that solutions obtained using the moving mesh method (MMM) are sufficiently accurate, and the absolute error is also much lower than the PINNs.

In this paper, we propose a linear, decoupled, unconditionally stable fully-discrete finite element scheme for the active fluid model, which is derived from the gradient flow approach for an effective non-equilibrium free energy. The developed scheme is employed by an implicit-explicit treatment of the nonlinear terms and a second-order Gauge–Uzawa method for the decoupling of computations for the velocity and pressure. We rigorously prove the unique solvability and unconditional stability of the proposed scheme. Several numerical tests are presented to verify the accuracy, stability, and efficiency of the proposed scheme. We also simulate the self-organized motion under the various external body forces in 2D and 3D cases, including the motion direction of active fluid from disorder to order. Numerical results show that the scheme has a good performance in accurately capturing and handling the complex dynamics of active fluid motion.