International Journal for Numerical Methods in Fluids最新文献

The present inquiry examines the necessity for enhanced thermal transfer approaches across multiple industrial domains, such as energy generation and processing of materials, through an investigation of the intricate dynamics of micropolar nanofluids. The main objective is to numerically simulate the Cattaneo–Christov heat flux in magnetohydrodynamics (MHD) to investigate the radiative behavior of Darcy–Forchheimer micropolar nanofluids, including the effects of activation energy. The study presumes steady-state conditions and employs particular constitutive equations to characterize the behavior of the nanofluid. The governing equations, which incorporate binary chemical interactions, radiation, and a thermal source, are reformulated with similarity variables into a system of nonlinear ordinary differential equations (ODEs). The BVP4C MATLAB software is utilized for obtaining numerical solutions. The study indicates that an increase in thermophoresis, thermal source, radiation, and Brownian motion factors improves thermal distributions in micropolar nanofluid flow. Moreover, increased radiation parameters result in a rise in the thermal transmission rate, while enhancing activation energy factors leads to a decrease. The findings are essential for enhancing temperature control in systems and for the development of efficient thermal appliances.

In this work, the control volume free element method (CVFrEM) is proposed for turbulent forced and natural convection problems. In the proposed method, the control volume at each collocation node is generated locally within the free element formed for the node, based on which the governing equations are discretized using the Green-Gauss formula. In contrast to conventional segregated SIMPLE-like algorithms, the newly proposed method achieves fully coupled velocity and pressure, thereby significantly improving convergence characteristics. The computational framework has been validated through the turbulent natural and forced convection problems involving conjugate heat transfer. Comprehensive verification has been carried out by systematically comparing numerical results with benchmark solutions from the literature and experimental measurements. Numerical experiments on several test cases demonstrate the computational efficiency of the proposed method and its numerical robustness.

The hyperbolic grid generation method is widely used for generating computational grids. Because of conflicts arising from various grid constraints, the traditional hyperbolic grid generation method faces challenges in guaranteeing the fulfillment of all orthogonal constraints among three directions during the grid generation. A new three-directional orthogonality preserving method (TDOP) is introduced in the present work to enhance the orthogonality of the computational grid during the grid generation process. Unlike the traditional grid generation method, TDOP takes all three orthogonal constraints into consideration, establishes a function to quantify the overall grid orthogonality, and subsequently derives new governing equations for grid generation by solving a constrained optimization problem. Compared with the traditional method, TDOP exhibits enhanced control over the orthogonality among three directions, thereby enabling the generation of a computational grid with better orthogonality. Three application cases are employed to demonstrate the effectiveness and superiority of TDOP in hyperbolic grid generation. Results indicate that, compared with the traditional method, TDOP can effectively prevent the emergence of highly skewed grids and enables enhanced optimization of orthogonality in the advancing front layer. Consequently, TDOP can generate a computational grid with better orthogonality and higher quality than the traditional method.

In this article, the spatial local discontinuous Galerkin (LDG) method and the temporal spectral deferred correction (SDC) method are combined to construct the higher-order approximating method for the unsteady rotating Navier–Stokes equations on the triangular mesh. First, the artificially compressible method is used to circumvent the incompressibility constraint, and the rotating Navier–Stokes equations are transformed into the artificially compressible rotating Navier–Stokes equations. Then, based on equal LDG interpolation and repeated temporal SDC, the higher-order fully discrete method is presented. Theoretically, the stability analysis of the second-order fully discrete method is provided, and it is shown that the time step $��\tau �$ is stable within the upper bound constraints. Numerical examples are presented to demonstrate the effectiveness of the proposed method.

By revisiting the derivation of multi-state HLL approximate Riemann solver for the ideal magneto-hydrodynamics, an extended HLLD Riemann solver is constructed based on the assumption that the normal velocity is constant over the Riemann fan, which is bounded by two fast waves, and separated by two compound waves and a middle contact wave. Compared with the HLLD solver, the slow waves are allowed to persist inside the Riemann fan, so that the two Alfvén waves are replaced by the two compound waves that are the merging product of the Alfvén and slow waves. Conseq uently, the corresponding wave speeds are chosen to be an interpolation between the Alfvén and slow waves for simplicity. The numerical tests showed that the extended HLLD solver (called HLLD-P) has better performance for the capture of slow waves than the HLLD solver, and exhibits overall better accuracy in some situations where the slow waves exist. However, the new solver does not capture the Alfvén wave as well as the HLLD solver once the estimated speeds of compound waves deviate from the Alfvén wave speeds. Overall, the HLLD-P solver is fully compatible with the HLLD solver as long as the compound waves degenerate to the Alfvén waves inside the Riemann fan. It is indicated that the HLLD-P solver can be used for the various applications of MHD simulation, especially for those cases where the slow waves are expected to be generated.