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With increasing global energy transition and environmental awareness, liquefied natural gas (LNG) is rapidly developing as an efficient and clean energy source. LNG pumps are widely used in industrial applications. This study focuses on the LNG pump and pipeline system, and it innovatively establishes a computational model based on weak compressible fluid in order to better reflect the characteristics of pressure pulsation and the flow situation. Through numerical simulations, the flow characteristics of the pump were analyzed. In addition, the flow conditions at the pipe tee were analyzed, and the attenuation patterns of pressure waves at different frequencies within the pipe were also investigated. The internal flow field of the pump was analyzed at three specific time points. The results indicate that, during the initial start-up phase, the internal flow state of the pump is complex, with significant vortices and pressure fluctuations. As the flow rate and rotational speed increase, the flow gradually stabilizes. Moreover, the pressure pulsation coefficient within the pipeline varies significantly with position.

When a traditional Weakly-Compressible Smoothed Particle Hydrodynamics (WCSPH) model is used to simulate free surface flow with a large Reynolds number, an unstable numerical calculation due to high random pressure oscillations will result, while an accurate pressure field is of vital significance for simulating violent fluid-structure interactions. Riemann-based SPH and Delta-SPH are widely used to solve this problem. In this paper, to enhance computational efficiency, the SPH method is implemented on a General Processing Unit (GPU) platform using Compute Unified Device Architecture (CUDA). Parallelized SPH programs including the standard SPH method, Riemann-based SPH and Delta-SPH are verified by a dam break model with large Reynolds number and violent deformation of free surfaces. The results show that all SPH methods can vividly reflect the whole process of splashing, rolling and backward jet flow; both the Riemann-based SPH and the Delta-SPH methods are effective in alleviating the problem of inhomogeneous pressure distribution in the simulation process; the Riemann-based SPH method has better stability even with relatively large particle spacing, and it has higher accuracy in simulating impact pressure. When the number of particles reaches 100,000, compared with a single-thread Central Processing Unit (CPU) implementation, the speedups obtained with NVIDIA Titan V with high computing cores and Quadro K2200 with low computing cores are thousands and hundreds, respectively.

Homogeneous isotropic turbulence (HIT) has been a useful theoretical concept for more than fifty years of theory, modelling, and calculations. Some exact results are revisited in incompressible HIT, with special emphasis on the 4/5 Kolmogorov law. The finite Reynolds number effect (FRN), which yields corrections to that law, is investigated, using both Kármán–Howarth-type equations and a statistical spectral closure of the Eddy-Damped Quasi-Normal Markovian (EDQNM)-type. This discussion offers an opportunity to give an extended review of such spectral closures, from weak turbulence, as in wave turbulence theory, to a strong one. Extensions of the 4/5 or 4/3 Kolmogorov/Monin laws to anisotropic cases, such as stably stratified and MHD turbulence, are briefly touched on. Before addressing more recent work on compressible isotropic turbulence, the simplest case of quasi-incompressible turbulence subjected to externally imposed isotropic compression or dilatation is presented. Rapid distortion theory is found to be a poor model in this isotropic case, in contrast with its relevance in strongly anisotropic flow cases. Accordingly, a fully nonlinear approach based on a rescaling of all fluctuating variables is used, in order to show its interplay with the linear operator. This opens the discussion on the cases of homogeneous incompressible turbulence, where RDT and nonlinear models are relevant, provided that anisotropy is accounted for. Finally, isotropic compressible flows of increasing complexity are considered. Recent studies using weak turbulence theory, modelling, and DNS are discussed. A final unpublished study involves interactions between the solenoidal mode, inherited from incompressible turbulence, and the acoustic and entropic modes, which are specific to the compressible problem. An approach to acoustic wave turbulence, with resonant triads, is revisited on this occasion.

Microfossils can have a large impact on the hydromechanical properties of marine sediments. Here, we study how these properties change in sediment mixtures containing varying concentrations of diatoms during experimental loading. We mixed an illite‐rich glaciomarine clay known as Boston Blue Clay (BBC) and a smectite‐rich marine clay known as Eugene Island Clay (EI) with marine and lacustrine diatoms in mass ratios of 100:00, 90:10, and 80:20. These mixtures were uniaxially compressed to 100 kPa in resedimentation tests and further loaded to 2 MPa in constant rate of strain consolidation experiments. We found that adding diatoms results in an increase in void ratio, compressibility, and vertical permeability at a given vertical effective stress for both sediments. These changes are due to an increased intraskeletal and interskeletal porosity caused by the porous nature of diatoms and their ability to form stress bridges. With increasing vertical effective stress, sediments lose their permeability at a slower rate when containing diatoms. These changes are most evident in BBC mixtures. When comparing both sediment types, void ratio and permeability decrease faster during burial for the EI mixtures than the BBC mixtures. These results provide new insights into the hydromechanical behavior of microfossil‐rich marine sediments and contribute to our understanding of their potential for overpressure generation and the development of a weak layer. Plain Language Summary Diatoms, which are single‐celled alga surrounded by a cell wall made from silica, are common in ocean sediments. Here, we study the mechanical and flow properties of sediments containing varying amounts of diatoms to understand their contribution to potential overpressure generation in the subsurface by carrying large quantities of pore water inside their skeleton to greater depths. We describe the effect of diatoms on porosity (volume of pore space between the particles) and permeability (ease with which fluid flows through sediments) and apply models commonly used in the scientific community. The results are beneficial for a better understanding of the hydromechanical behavior of diatomaceous mudstones and have implications for submarine slope stability. Key Points We determine the effects of diatoms on the compression and permeability behavior of marine mudstones through consolidation tests Diatoms increase the porosity, compression index, and permeability Diatoms provide vertical fluid pathways through connected intraskeletal porosity and pores preserved by diatom bridging

This paper is concerned with a compressible MHD equations describing the evolution of viscous non-resistive fluids in piecewise regular bounded Lipschitz domains. Under the general inflow-outflow boundary conditions, we prove existence of global-in-time weak solutions with finite energy initial data. The present result extends considerably the previous work by Li and Sun (J Differ Equ 267:3827–3851, 2019), where the homogeneous Dirichlet boundary condition for velocity field is treated. The proof leans on the specific mathematical structure of equations and the recently developed theory of open fluid systems. Furthermore, we establish the weak-strong uniqueness principle, namely a weak solution coincides with the strong solution on the lifespan of the latter provided they emanate from the same initial and boundary data. This basic property is expected to be useful in the study of convergence of numerical solutions.

Isothermal visco-elastodynamics in the Kelvin–Voigt rheology is formulated in the spatial Eulerian coordinates in terms of velocity and deformation gradient. A generally nonconvex (possibly also frame-indifferent) stored energy is admitted. The model involves a nonlinear 2nd-grade nonsimple (multipolar) viscosity so that the velocity field is well regular. To simplify analytical arguments, volume variations of the solid material are assumed to be only rather small so that the mass density is constant, exploiting the concept of semi-compressible materials. Existence of weak solutions is proved by using the Galerkin method combined with a suitable regularization, using nontrivial results about transport by smooth velocity fields.

In this paper, we study the dissipative measure-valued solution to the magnetohydrodynamic equations of 3D compressible isentropic flows with the adiabatic exponent γ > 1 and prove that a dissipative measure-valued solution is the same as the standard smooth classical solution as long as the latter exists, provided they emanate from the same initial data (weak–strong) uniqueness principle.

This paper concerns the energy conservation for the weak solutions of the compressible Navier–Stokes equations. Assume that the density is positively bounded, we work on the regularity assumption on the gradient of the velocity, and establish a Lp–Ls type condition for the energy equality to hold in the distributional sense in time. We mention that no regularity assumption on the density derivative is needed any more.

We consider the compressible Navier–Stokes system on time-dependent domains with prescribed motion of the boundary. For both the no-slip boundary conditions as well as slip boundary conditions we prove local-in-time existence of strong solutions. These results are obtained using a transformation of the problem to a fixed domain and an existence theorem for Navier–Stokes like systems with lower order terms and perturbed boundary conditions. We also show the weak–strong uniqueness principle for slip boundary conditions which remained so far open question.

In Colombeau (Z Angew Math Phys 66:2575–2599, 2015), Colombeau (Z Angew Math Phys 71:112, 2020) we constructed weak asymptotic solutions to some systems of fluid dynamics on the n -D torus T n . In Colombeau (Z Angew Math Phys 71:112, 2020), we passed to the limit by compactness to obtain Radon measures on T n that satisfy the equations in a natural sense as sum of distributions. The construction was done on physical ground and, though we obtained full rigorous mathematical proofs, we had to introduce arbitrary ingredients such as an approximation of the initial condition or a function to obtain bounds on the variables of density and velocity, which are used in the demonstrations. In this paper, from a more precise construction and under the assumptions of finiteness of velocity and absence of void region in the flow, we prove that the Radon measure limits are independent on all arbitrary ingredients used in their construction: they depend only on the initial condition ρ 0 ∈ L 1 ( T n ) , u 0 ∈ L ∞ ( T n ) n . We describe them as particular vanishing viscosity limits.