International Journal for Numerical Methods in Fluids最新文献

Pressure-based inverse design (ID) cannot converge in flow regimes with ultralow Reynolds numbers (Res). This study proposes a shear-stress-based ID method for airfoil design at Re = 1000 at the optimal angle of attack (AOA) in the presence of a laminar separation bubble. The proposed method applies the difference between the existing and target shear stress distributions (SSDs) to a deformable surface. The Navier–Stokes equations are solved to calculate the wall SSD during each iteration of the ID process. This process modifies the airfoil geometry until the abovementioned difference becomes negligible, achieving convergence to the target geometry. Achieving the maximum lift-to-drag ratio by manually correcting the wall SSD involves extensive trial and error, making it almost impossible. Thus, in the second part of this research, we trained Gaussian process regression and an ensemble of trees deep learning (DL) models using data generated during ID at the optimal AOA to predict lift and drag coefficients, respectively. The SSD was optimized throughout the ID process by coupling the DL models with a genetic algorithm (GA). Optimization was performed in several consecutive cycles, with the DL models becoming more accurate and updated as more data were gathered, helping the GA obtain the optimal SSD and geometry precisely. Finally, the performance curves of different geometries obtained through the optimization cycles were evaluated and compared using the Fluent solver. The results demonstrated a 22.42% increase in the lift-to-drag ratio relative to the initial population at the optimal AOA.

To achieve the high-precision characteristics within the smooth regions while maintaining stable, non-oscillatory, and sharp discontinuity transitions, the weighted essentially non-oscillatory (WENO) scheme and its variants have been developed. However, when there are multiple discontinuities close to each other, the numerical accuracy and robustness of the traditional schemes are probably affected. To this end, a hierarchical multi-resolution WENO (MR-WENO) scheme is proposed in the present study to suppress the overshoot and improve the accuracy of the original MR-WENO scheme in the vicinity of discontinuities. It could achieve an adaptive selection of the substencils and optimal accuracy due to the hierarchical strategy and the new smoothness indicator. The performances of the hierarchical MR-WENO scheme have been tested in 1D and 2D cases. The accuracy has been validated and the influences of weights of both large stencils and small substencils have been comprehensively discussed. The linear weights are adjusted aiming at improving the resolution of discontinuities and suppressing the unexpected weight oscillations. As a result, discontinuities like shock waves and contact discontinuities could be accurately resolved, while overshoot phenomena in the MR-WENO scheme are effectively suppressed in both 1D and 2D cases. Especially, the numerical error of the Lax problem has been reduced by one or two orders of magnitude in the vicinity of discontinuities. With an implementation of the KXRCF indicator, the computational cost has been controlled while maintaining the present superiority of shock capturing capacity.

The one-dimensional Richards equation has been widely employed to model water flow in porous media, but the effect of averaging soil diffusivity/hydraulic conductivity on the computed solutions has received comparatively less attention than the numerical approaches to solve the equation. The use of non-arithmetic (harmonic and geometric) averaging of diffusivity in finite volume simulations of the Richards equation is known to produce numerical artifacts that include the lagging of the wetting front in time and even “locked” fronts with no flow, depending on the type of soil and the constitutive relation. In this work, we propose a new and simple approach to define the interfacial diffusivity or hydraulic conductivity based on “modified” non-arithmetic averages that mitigates the spurious artifacts at minimal computational cost. Numerical studies with unsaturated soils using different soil diffusivity models (for horizontal infiltration) and different hydraulic conductivity models (for vertical infiltration) conclusively demonstrate that the $��m�$-harmonic and $��m�$-geometric averages defined in this work lead to physically consistent solutions of the Richards equation.

Double-tube heat exchangers using ferrofluids under magnetic fields, which induce vortices, improve heat transfer and reduce irreversibilities. This study analyzes heat transfer and entropy generation of Fe₃O₄/water in a double-tube heat exchanger at Re = 100, subjected to magnetic fields. Key parameters, including inner tube cross-sectional geometry and magnetic field characteristics (intensity, wire distance, configuration, and number), are examined and optimized. The flow structure, heat transfer, friction factor coefficient, performance evaluation criterion (PEC), and entropy generation are evaluated based on thermodynamic principles. A finite volume numerical code is developed to solve the governing equations and consider the magnetic field through a UDF code on thermal and entropy performance using the SIMPLE algorithm. The investigation is evaluated: (1) the impact of the inner tube's cross-sectional geometry, (2) the effect of the current-carrying wire and outer tube distance, and (3) the influence of the magnetic field's arrangement and number. Altering the cross-sectional geometry shows that a vertically elliptical shape increases heat transfer by 81%, while the horizontally elliptical shape achieves the best overall performance. Adjusting the wire distance to d/r₀ = 0.125 offers better overall operational performance by considering the heat transfer and entropy simultaneously. Additionally, a horizontal arrangement with two magnetic fields, which represents the optimal configuration, improves heat transfer and pressure drop by 2.8 and 21 times at Mn = 2 × 10¹⁰, and enhances the PEC by 39%. These findings can be applied in the field of energy system optimization, especially where compact design and high thermal efficiency are critical requirements.

In this article, a cell-centered discontinuous Galerkin (DG) method is presented for solving Lagrangian radiation hydrodynamic equations (RHE). The equations are separated into a hydrodynamic part and a radiation diffusion part. These two parts are written in Lagrangian forms. The hydrodynamic part is discretized by a cell-centered DG scheme in reference space using Taylor basis functions. An approximate Riemann solver is used for the velocity of vertices, and the radiation diffusion is solved using an interior penalty method. Due to the deformation of the basis functions in physical space, curvilinear mesh is formed. Numerical tests are presented to show its accuracy and robustness.

This paper presents an optimization algorithm designed to effectively handle a new general class of the nonlinear variable-order fractional partial differential equations (GCNV-OFPDEs) with nonlocal boundary conditions. Our approach involves utilizing a novel variant of the polynomials, namely generalized Abel polynomials (GAPs), and also new operational matrices to approximate the solution of the GCNV-OFPDEs. A key aspect of our algorithm is the transformation of GCNV-OFPDEs, along with their respective nonlocal boundary conditions, into systems of nonlinear algebraic equations. By solving these systems, we can determine the unknown coefficients and parameters. To address the nonlinear system, we employ the Lagrange multipliers to achieve optimal approximations. The convergence analysis of the approach is discussed. To validate the effectiveness of our algorithm, we conducted numerous experiments using various examples. The results obtained demonstrate the exceptional accuracy of our approach and its potential for extension to more complex problems in the future.

This paper presents a novel mesh-free approach for solving the Navier–Stokes equations. The method makes use of the meshless method of fundamental solutions (MFS) and the Monte Carlo integration technique for computing the domain integral of the convective terms. No domain or boundary discretization is required. This approach facilitates numerical computation while ensuring accuracy and stability. By imposing a penalty parameter, the Navier–Stokes equations are transformed to resemble the Navier equations of elasticity. Hence, elasticity based fundamental solutions are employed. The proposed formulation is validated through numerical examples, demonstrating its efficacy in capturing steady-state flow phenomena through several examples. This highly parallelized system is then accelerated via GPU computing. Overall, the proposed method provides a promising paradigm for advancing computational fluid mechanics, offering a versatile framework with broad applicability in engineering and scientific domains.