Computers & Fluids最新文献

We aim at computing time- and span-periodic flow fields in span-invariant configurations. The streamwise and cross-stream derivatives are discretised with finite volumes while time and the span-direction are handled with pseudo-spectral Fourier-collocation methods. Doing so, we extend the classical Time Spectral Method (TSM) to a Space–Time Spectral Method (S-TSM), by considering non-linear interactions of a finite number of time and span harmonics. For optimisation, we introduce an adjoint-based framework that allows efficient computation of the gradient of any cost functional with respect to a large-dimensional control parameter. Both theoretical and numerical aspects of the methodology are described: evaluation of matrix–vector products with S-TSM Jacobian (or its transpose) by algorithmic differentiation, solution of fixed-points with quasi-Newton method and de-aliasing in time and space, solution of direct and adjoint linear systems by iterative algorithms with a block-circulant preconditioner, performance assessment in CPU time and memory. We illustrate the methodology on the case of 3D instabilities (first Mack mode) triggered within a developing adiabatic boundary layer at M = 4.5. A gradient-ascent method allows to identify a finite-amplitude 3D forcing that triggers a non-linear response exhibiting the strongest time- and span-averaged drag on the flat-plate. In view of flow control, a gradient-descent method finally determines a finite amplitude 2D wall-heat flux that minimises the averaged drag of the plate in presence of the previously determined non-linear optimal forcing.

In this study, we employed a non-orthogonal, three-dimensional, multi-relaxation-time pseudo-potential lattice Boltzmann method, and investigate the behaviors of droplets impacting chemically patterned surfaces. We considered two interfaces: a hydrophobic/neutral strip on a hydrophilic wall (surface A), and a hydrophilic strip on a hydrophobic wall (surface B). The dynamics of impact, including the evolution of the morphology and the droplet spreading factor, were investigated under the influence of the difference in wettability, Weber number (We), and strip width. An increase in the wettability difference of surface A delayed droplet detachment and reduced the amplitude of oscillations, where this can be attributed to the surface tension and viscous dissipation, which had more time to weaken the strength of the jet. The magnitude of droplet detachment time initially increased with We but eventually decreased. As We is further increased, the ratio of viscous loss to the initial kinetic energy of the droplet is decreased and resulted in a shorter detachment time. The unbalanced Young's force significantly affected the evolution of the droplet on surface B. The mass of the droplet accumulated near the borderline of the strip and expanded along the y-axis under the influence of the inertial force, where this led to a larger spreading factor along the y-axis. In addition, the mass of the droplet on the hydrophobic wall affected the strength of the unbalanced Young's force. As the strip width increased, the spreading factor initially increased but then decreased along the y-axis owing to the combined action of inertial forces.

The effects of particles on the Richtmyer–Meshkov (RM) instability of a flat interface driven by perturbed and reflected shock waves are numerically investigated. By utilizing three different sizes of particles ($d=5\mu m$, $20\mu m$ and $50\mu m$) and two types of heavy gases (SF₆ and CO₂), the effect of the presence of particles with different sizes on the RM instability and the dynamic process of particle diffusion have been explored, respectively. The evolution of interface morphology under smaller particle ($d=5\mu m$ and $20\mu m$) conditions bears a striking resemblance to that of the condition without particles while the large particles ($d=50\mu m$) contribute to the formation of many “wrinkles” on the interface due to the large particle size and particle inertia. The addition of particles with smaller size ($d=5\mu m$ and $20\mu m$) can either slightly inhibit or promote the growth of the mixing width at the late stage of the interface evolution, depending on the extent of interface evolution. Both the particle size and the type of heavy fluid are able to influence the particle motion.

This article provides a series of high-order multi-resolution trigonometric weighted essentially non-oscillatory schemes with adaptive linear weights for solving hyperbolic conservation laws in a finite difference framework, which are termed as the MR-TWENO-ALW schemes. These new TWENO schemes only use the information defined on two unequal-sized spatial stencils and do not need to introduce other stencils to achieve optimal high-order accuracy. To increase the flexibility of the linear weights, we design an adaptive linear weight process which is an automatic adjustment of two linear weights with two simple conditions. This ensures the schemes to get the optimal order of accuracy in smooth regions, accurately approximate sharp gradients, and suppress high oscillations near strong discontinuities. These new MR-TWENO-ALW schemes can achieve high spectral resolution and maintain low computational cost in large scale engineering applications. And these new schemes are simple in the construction and could be extended to arbitrarily high-order accuracy on other computing meshes. Extensive one-dimensional and two-dimensional numerical examples are used to testify the feasibility of these new MR-TWENO-ALW schemes.

Geometric flux-based Volume-of-Fluid (VOF) methods (Marić et al., 2020) are widely considered consistent in handling two-phase flows with high density ratios. However, although the conservation of mass and momentum is consistent for two-phase incompressible single-field Navier–Stokes equations without phase-change (Liu et al., 2023), discretization may easily introduce inconsistencies that result in very large errors or catastrophic failure. We apply the consistency conditions derived for the $\rho$LENT unstructured Level Set/Front Tracking method (Liu et al., 2023) to flux-based geometric VOF methods (Marić et al., 2020), and implement our discretization into the plicRDF-isoAdvector geometrical VOF method (Roenby et al., 2016). We find that computing the mass flux by scaling the geometrically computed fluxed phase-specific volume can ensure equivalence between the mass conservation equation and the phase indicator (volume conservation) if consistent discretization schemes are chosen for the temporal and convective term. Based on the analysis of discretization errors, we suggest a consistent combination of the temporal discretization scheme and the interpolation scheme for the momentum convection term. We confirm the consistency by solving an auxiliary mass conservation equation with a geometrical calculation of the face-centered density (Liu et al., 2023). We prove the equivalence between these two approaches mathematically and verify and validate their numerical stability for density ratios within [1, $10^6$] and viscosity ratios within [$10^2$, $10^5$].

Miscible density-driven convection in porous media has important implications for the long-term security of geological ${\text{CO}}_2$ sequestration. In this study, a REV-scale lattice Boltzmann equation method based on the generalized Navier–Stokes equations was used to simulate density-driven convection in porous media, Thus, the effects of the Rayleigh number, the Darcy number, the Schmidt number, and the porosity of porous media can be discussed separately. The results show that density-driven convection only occurs when the Rayleigh–Darcy–Schmidt number ${\text{Ra}}_{\text{D-S}}$ exceeds $10^2$. The larger the Ra, the more disordered the concentration field, the earlier the convective phenomenon begins, and the more significant the convective mixing; The larger the Da, the finer the generated fingers. These findings provide important insights for the development of geological sequestration technologies.

State-of-the-art predictions of the solar-wind and space weather phenomena are today largely based on the equations of magnetohydrodynamics (MHD). Despite their sophistication and success, the forecasting potential of global MHD models is often undermined by uncertainties in model inputs; the initial and boundary conditions are generally not known and must be estimated. This study therefore investigates the use of data assimilation strategies to minimize forecast errors in the context of initial-value problems of the one-dimensional ideal MHD equations. Several canonical MHD wave propagation problems involving both smooth and discontinuous solutions, including those having strongly non-linear behaviour with shocks, are considered in a set of twin experiments with varying synthetic observational data sparsity. Two data assimilation strategies are quantitatively compared, namely the Ensemble Kalman Filter (EnKF) and strong-constraint variational data assimilation. For the latter, the necessary adjoint model is derived, summarized, and validated. The study represents the first use of variational data assimilation applied to ideal magnetohydrodynamics and demonstrates its potential advantages over sequential approaches. In particular, for the numerical experiments considered herein, it is found that the variational approach consistently achieved superior performance and stability compared to the EnKF method. In addition, two different strategies for mitigating data assimilation induced errors associated with violation of the divergence-free property of the magnetic field are introduced and assessed. Finally, the present study provides the technical background and quantitative justification for future investigations of variational data assimilation aimed at enhancing three-dimensional simulations of the solar wind and space weather processes.

Two quantum algorithms are presented for the numerical solution of a linear one-dimensional advection–diffusion equation with periodic boundary conditions. Their accuracy and performance with increasing qubit number are compared point-by-point with each other. Specifically, we solve the linear partial differential equation with a Quantum Linear Systems Algorithm (QLSA) based on the Harrow–Hassidim–Lloyd method and a Variational Quantum Algorithm (VQA), for resolutions that can be encoded using up to 6 qubits, which corresponds to $N=64$ grid points on the unit interval. Both algorithms are hybrid in nature, i.e., they involve a combination of classical and quantum computing building blocks. The QLSA and VQA are solved as ideal statevector simulations using the in-house solver QFlowS and open-access Qiskit software, respectively. We discuss several aspects of both algorithms which are crucial for a successful performance in both cases. These are the accurate eigenvalue estimation with the quantum phase estimation for the QLSA and the choice of the algorithm of the minimization of the cost function for the VQA. The latter algorithm is also implemented in the noisy Qiskit framework including measurement noise. We reflect on the current limitations and suggest some possible routes of future research for the numerical simulation of classical fluid flows on a quantum computer.

Recently, the general synthetic iterative scheme (GSIS) has been proposed to find the steady-state solution of the Boltzmann equation in the whole range of gas rarefaction, where its fast-converging and asymptotic-preserving properties lead to the significant reduction of iteration numbers and spatial cells in the near-continuum flow regime. However, the efficiency and accuracy of GSIS have only been demonstrated in two-dimensional problems with small numbers of spatial cells and discrete velocities. Here, a large-scale parallel computing strategy is designed to extend the GSIS to three-dimensional flow problems, including the supersonic flows which are usually difficult to solve by the discrete velocity method. Since the GSIS involves the calculation of the mesoscopic kinetic equation which is defined in six-dimensional phase-space, and the macroscopic high-temperature Navier–Stokes–Fourier equations in three-dimensional physical space, the proper partition of the spatial and velocity spaces, and the allocation of CPU cores to the mesoscopic and macroscopic solvers, are the keys to improving the overall computational efficiency. These factors are systematically tested to achieve optimal performance, up to 100 billion spatial and velocity grids. For hypersonic flows around the Apollo reentry capsule, the X38-like vehicle, and the space station, our parallel solver can obtain the converged solution within one hour.

Immersed boundary method (IBM) is widely used for simulating flow in complex geometries using structured grids. However, this entails a disadvantage when simulating internal flows through curved and bent tubes. The presence of grids outside the fluid domain leads to the wastage of memory and computational overheads. Here, we propose a multi-block-multi-mesh framework to capture the complex geometry using multiple grid blocks fitted close to the body, reducing excess grids. This also has the advantage of using different and non-uniform grid spacing in different blocks. The reduction of the grid enables encompassing bigger caseloads on a single GPU. The solver is accelerated on GPU using OpenACC, compared to sequential CPU simulations, and speedup is presented. The speedup obtained is comparable to that of large multicore systems. The framework is extensively validated for straight artery with axisymmetric stenosis and bileaflet mechanical heart valve with axisymmetric sinus. This framework then models complex arterial flows like stenosed aorta, patient-specific branched aorta, bileaflet mechanical heart valve with Valsalva sinus and aorta, and lastly, patient-specific iliac aortic aneurysm. This framework achieves a significant reduction in GPU memory requirement for complex arterial models, enabling us to perform direct numerical simulation (DNS) of the stenosed aorta and mechanical heart valve cases in a single GPU.