A non-reflecting wave equation through directional wave-field suppression and its finite difference implementation

The acoustic wave equation describes wave propagation directly from basic physical laws, even in heterogeneous acoustic media. When numerically simulating waves with the wave equation, contrasts in the medium parameters automatically generate all scattering effects. For some applications - such as propagation analysis or certain wave-equation based imaging techniques - it is desirable to suppress these reflections, as we are only interested in the transmitted wave-field. To achieve this, a modification to the constitutive relations is proposed, yielding an extra term that suppresses waves with reference to a preferred direction. The scale-factor $$\alpha$$ α of this extra term can either be interpreted as a penetration depth or as a typical decay time. This modified theory is implemented using a staggered-grid, time-domain finite difference scheme, where the acoustic Poynting-vector is used to estimate the local propagation direction of the wave-field. The method was successfully used to suppress reflections in media with bone tissue (medical ultrasound) and geophysical subsurface structures, while introducing only minor perturbations to the transmitted wave-field and a small increase in computation time.

Generalized eigenproblem without fermion doubling for Dirac fermions on a lattice

The spatial discretization of the single-cone Dirac Hamiltonian on the surface of a topological insulator or superconductor needs a special ``staggered’’ grid, to avoid the appearance of a spurious second cone in the Brillouin zone. We adapt the Stacey discretization from lattice gauge theory to produce a generalized eigenvalue problem, of the form \bm{\mathcal H}\bm{\psi}=\bm{E}\bm{\mathcal P}\bm{\psi}ℋ𝛙=𝐄𝒫𝛙, with Hermitian tight-binding operators \bm{\mathcal H}ℋ, \bm{\mathcal P}𝒫, a locally conserved particle current, and preserved chiral and symplectic symmetries. This permits the study of the spectral statistics of Dirac fermions in each of the four symmetry classes A, AII, AIII, and D.

The hindcast of recent tsunamis in Northern Pacific

Three earthquakes occurred in the North Pacific in 2020, causing observable tsunamis. The tsunamis were not devastating. Numerical modelling of tsunami propagation was performed to reproduce operational forecasting (retrospective analysis) of waveforms at deep-water stations. Direct calculation of tsunami using USGS finite-fault source data on GPU was carried out. The leap-frog (Arakawa staggered grid) scheme calculation over the Pacific Ocean on a regular grid with a spatial step of 0.5 arc minutes of 1440 min (1 day) tsunami propagation was performed in approximately 90 min of computer time. With use of a hybrid cluster with several GPU accelerators and proper optimization of the simulation algorithm, this time can be reduced by tens of times. Consequently, the time for estimating the transfer function will be comparable to the travel time of a tsunami to the stations, where the forecasts data is. It will make possible to forecast the shape of a tsunami at any point with a lead time enough to decide for tsunami alert at sites where a tsunami poses a real danger. The calculation results are in good agreement with the real data of deep-ocean measurements. The quality of the forecast is comparable to the quality of calculations by other methods.

An Atomization Model of Air Spraying Using the Volume-of-Fluid Method and Large Eddy Simulation

When painting complex surfaces, such as large-curvature surfaces, poor coating quality is often obtained, which may be caused by lack of an appropriate atomization model, insufficient understanding of atomization mechanisms and laws, and improper painting parameters. This paper presents a numerical model of paint atomization of air spraying using the volume-of-fluid method and large eddy simulation. The interface capture and the turbulent flow were mainly considered in the model: the former was tracked by the volume-of-fluid method and the latter was predicted by the large eddy simulation. After the computational domain being meshed by the staggered-grid method, the governing equations were discretized by the finite volume method and were solved by the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) Consistent algorithm. The results of numerical simulations show that the characteristics of atomization flow field, such as velocity variation, pressure distribution, and paint volume fraction are in agreement with the regularities of atomization. Moreover, the primary and secondary atomization phenomena can be clearly observed: as soon as the paint issues from the nozzle, the paint flow begins to distort and the paint fragments continuously eject from the main paint flow and then these paint fragments distort and disintegrate into smaller elements. A comparison with the experimental data from the literature proves that the model of the whole atomization process of air spray is effective. The model is suitable for simulating the whole atomization process and easy to obtain initial conditions, which can be applied to set the appropriate painting parameters and study paint atomization mechanisms and laws in depth.

The Characteristics of Seismic Rotations in VTI Medium

Under the assumptions of linear elasticity and small deformation in traditional elastodynamics, the anisotropy of the medium has a significant effect on rotations observed during earthquakes. Based on the basic theory of the first-order velocity-stress elastic wave equation, this paper simulates the seismic wave propagation of the translational and rotational motions in two-dimensional isotropic and VTI (transverse isotropic media with a vertical axis of symmetry) media under different source mechanisms with the staggered-grid finite-difference method with respect to nine different seismological models. Through comparing the similarities and differences between the translational and rotational components of the wave fields, this paper focuses on the influence of anisotropic parameters on the amplitude and phase characteristics of the rotations. We verify that the energy of S waves in the rotational components is significantly stronger than that of P waves, and the response of rotations to the anisotropic parameters is more sensitive. There is more abundant information in the high-frequency band of the rotational components. With the increase of Thomsen anisotropic parameters ε and δ, the energy of the rotations increases gradually, which means that the rotational component observation may be helpful to the study of anisotropic parameters.

The Momentum Conserving Scheme Implementation for Simulating Dambreak Flow in a Channel with Various Contractions

Rapid flow downstream due to dambreak has a detrimental effect on the surrounding environment or, more dangerously, can be life-threatening. From a practical point of view, these flows are important to studies due to the limited dambreak real case data. This paper discusses the numerical modelling of the dambreak flow through a channel with three different contractions. Our goal here is to investigate the performance of a numerical model for solving the Saint-Venant equations using a momentum conserving staggered grid scheme (MCS). The scheme is the conservative formulation of the governing equations. Flows across channels of various widths and depths have been successfully simulated using a version of this scheme. In this work, we extend our previous work by simulating dambreak flow in a wave tank through several forms of contraction; trapezoidal and triangular. Our simulation results show good agreement with the experimental data in the literature. This assessment shows the merit of the scheme, which is suitable for dambreak flows in channels of varying width.

Numerical simulation of non-Newtonian Carreau fluid in a lid-driven cavity

In this work, the 2D lid-driven cavity flow of non-Newtonian Carreau fluids has been studied by finite difference method on a staggered grid. A finite-difference algorithm on staggered grid based on projection method is adopted to solve the lid-driven cavity flow, which includes a second-order central difference scheme for the non-Newtonian viscous stress term. This study has been conducted for the certain pertinent parameters of Reynolds number (Re=100-1000), power-law index (n=0.6-1.4). The results show that as the Reynolds number increases, the influence of the power-law index on the flow increases. As the power-law index decreases, the flow field becomes more complicated.

Finite Volume Simulation of Natural Convection for Power-Law Fluids with Temperature-Dependent Viscosity in a Square Cavity with a Localized Heat Source

In this paper, numerical study on natural convection heat transfer for confined thermo-dependent power-law fluids is conducted. The geometry of interest is a fluid-filled square enclosure where a uniform flux heating element embedded on its lower wall is cooled from the vertical walls while the remaining parts of the cavity are insulated, without slipping conditions at all the solid boundaries. The governing partial differential equations written in terms of non-dimensional velocities, pressure and temperature formulation with the corresponding boundary conditions are discretized using a finite volume method in a staggered grid system. Coupled equations of conservation are solved through iterative Semi Implicit Method for Pressure Linked Equation (SIMPLE) algorithm. The effects of pertinent parameters, which are Rayleigh number (103 ≤ Ra ≤ 106), power-law index (0.6 ≤ n ≤ 1.4), Pearson number (0 ≤ m ≤ 20) and length of the heat source (0.2 ≤ W ≤ 0.8) on the cooling performance are investigated. The results indicate that the cooling performance of the enclosure is improved with increasing Pearson and Rayleigh numbers as well as with decreasing power-law index and heat source length.