International Journal for Numerical Methods in Fluids最新文献

Engineering simulations are usually based on complex, grid-based, or mesh-free methods for solving partial differential equations. The results of these methods cover large fields of physical quantities at very many discrete spatial locations and temporal points. Efficient compression methods can be helpful for processing and reusing such large amounts of data. A compression technique is attractive if it causes only a small additional effort and the loss of information with strong compression is low. The paper presents the development of an incremental singular value decomposition (SVD) strategy for compressing time-dependent particle simulation results. The approach is based on an algorithm that was previously developed for grid-based, regular snapshot data matrices. It is further developed here to process highly irregular data matrices generated by particle simulation methods during simulation. Various aspects important for information loss, computational effort, and storage requirements are discussed, and corresponding solution techniques are investigated. These include the development of an adaptive rank truncation approach, the assessment of imputation strategies to close snapshot matrix gaps caused by temporarily inactive particles, a suggestion for sequencing the data history into temporal windows as well as bundling the SVD updates. The simulation-accompanying method is embedded in a parallel, industrialized smoothed-particle hydrodynamics software and applied to several 2D and 3D test cases. The proposed approach reduces the memory requirement by about 90% and increases the computational effort by about 10%, while preserving the required accuracy. For the final application of a water turbine, the temporal evolution of the force and torque values for the compressed and simulated data is in excellent agreement.

Heat transfer in magnetically confined plasmas is characterized by extremely high anisotropic diffusion phenomena. At the core of a magnetized plasma, the heat conductivity coefficients in the parallel and perpendicular directions of the induction field can be very different. Their ratio can exceed $��1�{�0�}^{�8�}�$, and the pollution by purely numerical errors can make the simulation of the heat transport in the perpendicular direction very difficult. Standard numerical methods, generally used in the discretization of classical diffusion problems, are rather inefficient. The present paper analyzes a finite element approach for the solution of a highly anisotropic diffusion equation. Two families of finite elements of class $��{�𝒞�}^{�1�}�$, namely bi-cubic Hermite-Bézier and reduced cubic Hsieh-Clough-Tocher finite elements, are compared. Their performances are tested numerically for various ratios of the diffusion coefficients, on different mesh configurations, even aligned with the induction field. The time stepping is realized by an implicit high-order Gear finite difference scheme. An example of a reduced model is also provided to comment on some obtained results.

The modeling of fluids is an important field for mechanics of materials. In this work, we demonstrate that Hamilton's principle, which is well-known for the modeling of solids, can also be formulated to derive the Navier–Stokes equations, which paves the way for easy inclusion of complex material constraints. Furthermore, we expand Hamilton's principle to enable the introduction of “internal variables”, which describe the space- and time-dependent evolution of the material properties. Hereby, a novel strategy for the modeling of non-Newtonian fluids is given. Eventually, Hamilton's principle inherently enables a space-time formulation with the automatic derivation of the correct formal functional setting, which covers different scales of viscosity through the internal variable. The resulting system is a space-time multiscale model for fluid flow, which is based on an additional partial differential equation. The model constitutes thus a much more adaptive description of the complex processes in non-Newtonian fluid flow as possible for classical models based on algebraic constitutive laws. This also includes a spatially and temporally local evolution of the effective viscosity, depending on the local flow conditions rather than material parameters and resulting in both shear-thinning and shear-thickening behavior. Numerical examples substantiate our proposed setting by some studies from Newtonian flow to non-Newtonian regimes with fading or increasing viscosity.

Computational efficiency of vortex particle methods (VPMs) is hindered by the particle count increasing in simulation time. To reduce the number of computational elements, two algorithms are presented that downsample the discretized vorticity field representation in two-dimensional variable-core-size VPMs. The two methods are based on existing schemes of particle merging and regridding, and are adapted to follow a compression parameter set a priori. The effectiveness of the schemes is demonstrated on two benchmark cases of external flow: A stationary Lamb-Oseen vortex and an advecting vortex dipole. In both cases, compression is associated with a drastic reduction in particle count and computation time at a cost of diffusive errors in the vorticity field. Crucially, for gentle compression steps applied at appropriate intervals, the immediate errors in the vorticity field are comparable to reference cases despite great improvements in computational time. To examine the long-term impact of compression on accuracy and performance, it is recommended that repeated compressive steps be tested on more complex cases of bluff-body wakes, with a focus on the impact of downsampling on surface forces.

We present a novel meshless Lagrangian method for numerically solving the barotropic vorticity equation on a rotating sphere, an essential model in geophysical fluid dynamics. Our approach combines a particle-based discretization with a Discretization Corrected Particle Strength Exchange (DCPSE) operator, offering a consistent and accurate approximation of differential operators on unstructured node distributions. The method is implemented in a fully Lagrangian framework, inherently conserving circulation and enabling straightforward adaptation to complex geometries. We validate the proposed scheme against standard test cases for global circulation and Rossby-Haurwitz waves. The results demonstrate excellent agreement with reference solutions obtained from high-resolution spectral and finite difference models. In particular, our method captures the essential dynamics of the vorticity field with high fidelity and low numerical diffusion, while exhibiting convergence and stability properties suitable for long-term integrations. This study highlights the potential of meshless Lagrangian techniques in large-scale geophysical simulations. These techniques provide an alternative to traditional grid-based approaches and facilitate the natural handling of adaptive and irregular node distributions.