International Journal for Numerical Methods in Fluids最新文献

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.

This paper presents a comprehensive numerical investigation of the performance of pulsating heat pipes (PHPs) within nuclear reactor cooling systems. A volume of fluid (VOF) method was used to simulate the complex multiphase flow, providing detailed insights into fluid distribution, phase interactions, and temperature variations under different operating conditions. The simulations revealed distinct phase separation and convective flow patterns that enhance heat transfer efficiency, which is critical for optimizing thermal management in nuclear reactors. Additionally, artificial neural network (ANN) models were employed to predict volume fractions and wall temperatures, achieving high accuracy with R² values of 0.99 and 0.98, respectively, and low mean absolute errors (MAE). The ANN models also reduced computational time by 90% compared to traditional numerical simulations. These findings highlight the potential of PHPs to improve heat transfer in nuclear systems and demonstrate the practicality of ANN models for real-time thermal optimization. The research contributes to enhancing the safety and efficiency of nuclear reactor cooling systems, with broader implications for thermal management across various engineering applications.

We construct novel flux approximation schemes for the semidiscretized incompressible Navier–Stokes equations by finite-volume method on a staggered mesh. The calculation of the cell-face fluxes has been done by solving appropriate local non-linear boundary value problems (BVP). Consequently, the cell-face fluxes are represented as the sum of a homogeneous and an inhomogeneous flux; the homogeneous part represents the contribution of convection and viscous-friction, while the inhomogeneous part represents the contribution of the source terms. We derive three flux approximation schemes to include the impact of the source terms on the numerical fluxes. The first one is based on a homogeneous 1-D local BVP without source. The second scheme is based on an inhomogeneous 1-D local BVP considering only the pressure gradient term in the source. Finally, a complete flux scheme is derived which is based on an inhomogeneous 2-D local BVP. It takes into account both the gradient of the cross-flux and the pressure gradient in the source term. The numerical validation of the schemes is done for the benchmark lid-driven cavity flow for considerably high $��\text{Reynolds}�$ numbers along with a numerical convergence test for the exact solution of the Taylor–Green vortex problem.

We consider the moving least squares method to solve compressible two-phase water-water vapor flow with surface tension. A diffuse interface model based on the Navier–Stokes and Korteweg equations is coupled with a suitable system of state equations that allows for a more realistic estimation of the pressure jump across the liquid–vapor interface as a function of temperature. We propose a simple formulation for computing the capillarity coefficient $��\lambda �$ based on the surface tension and the thickness of the diffuse interface. A convergence analysis using pressure jump in the test case of static bubble is conducted to verify our solver. We present several numerical test cases that illustrate the ability of our model to reproduce qualitatively and quantitatively the effects of surface tension on cavitation bubbles in general situations.

High computational complexity due to rapidly increasing numerical stiffness is a difficult problem for simulating a supersonic reactive flow by using the uncoupled method. On the basis of our previous work, this paper proposes a dual adaptive method to ensure high calculation efficiency and good robustness in simulating stiff cases. The principle of this method is to realize adaptive coordination for the advection and reaction time steps in accordance with the non-uniform feature of stiffness in the space and time dimensions. The proposed method can advance by a small time step in strong stiffness while with a large one in weak stiffness through the “prediction-correction-recovery” strategy. Some classical problems are chosen to verify the performance of the proposed method. The proposed method improved the computation efficiency by at least $��30�\%�$ comparing with the previous method [1] and widened the error tolerance of the initial time step.

The seepage equation plays a crucial role in fields such as groundwater management, petroleum engineering, and civil engineering. Currently, physical-informed neural networks (PINNs) have become an effective tool for solving seepage equations. However, practical applications often involve variable flow rates, which pose significant challenges for using neural networks to find solutions. Inspired by Deep Operator Network (DeepONet), this paper proposes a new model named Simulation Net (Sim-net) to deal with unsteady sources or sinks problems. Sim-net is designed to simulate and solve seepage equations without the need for retraining. This model integrates potential spatial and temporal features based on spatial pressure distribution and well bottom–hole pressure, respectively, which serve as additional signposts to guide neural networks in approximating seepage equations. Sim-net exhibits transfer learning capabilities, enabling it to handle variable flow rate problems without retraining for new flow conditions. Numerical experiments demonstrate that the trained model can directly solve seepage equations without the need for retraining, indicating its superior applicability compared to existing PINNs-based methods. Additionally, in comparison to the DeepONet, Sim-net achieves higher accuracy.