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In order to investigate the impact of increasing the vertical resolution of the initial field on the 12–24 h forecasts of the TRAMS (Tropical Regional Atmosphere Model System) model, this study conducted numerical experiments focusing on a typical coastal warm sector rainfall event that occurred in the South China. The findings indicate that increasing the vertical resolution of the initial field led to improved simulation of coastal convection during the 0–12 h period. However, spurious convection was observed over the sea surface and continued to intensify in the 12–24 h period. Subsequent analysis revealed that the spurious convection is primarily associated with the hydrostatic adjustment of initial potential temperature in the TRAMS model. The hydrostatic adjustment leads to a reduction in the stability of the initial temperature stratification in the lower layers of the model, particularly when the number of vertical layers in the initial field increased from 17 to 32. A noticeable spurious unstable layer emerged between 0–200 m over the sea surface, triggering false convection. Further investigation revealed that the area where this unstable stratification occurs over the sea is situated below the height of the lowest level of the input analysis field (1000 hPa), indicating that the spurious disturbances are caused by an unreasonable vertical extrapolation process. Therefore, the findings of this study indicate that the extrapolation calculations using cubic splines in the initialization module of the TRAMS model introduce significant errors. Moreover, these errors increase with the enhancement of the vertical resolution of the initial field, which limits the improvement in model forecasting that could be achieved by increasing the vertical resolution of the initial field. We found that increasing the vertical resolution of the initial field in the TRAMS model led to spurious convection. This spurious convection is triggered by a false unstable layer near the surface. The computational errors during the hydrostatic adjustment of the initial perturbed potential temperature resulted in this false unstable layer.

Standard discontinuous Galerkin finite element solutions to convection-dominated convection–diffusion equations usually possess sharp layers but also exhibit large spurious oscillations. Slope limiters are known as a post-processing technique to reduce these unphysical values. This paper studies the application of deep neural networks for detecting mesh cells on which slope limiters should be applied. The networks are trained with data obtained from simulations of a standard benchmark problem with linear finite elements. It is investigated how they perform when applied to discrete solutions obtained with higher order finite elements and to solutions for a different benchmark problem.

When a hydrogen or oxygen bubble is created on the surface of an electrode, a micro-convective vortex flow due to the Marangoni effect is generated at the bottom of the bubble in contact with the electrode. In order to study such a phenomenon numerically, it is necessary to be able to simulate the surface tension variations along with a liquid-gas interface, to integrate the mass transfer across the interface from the dissolved species present in the electrolyte to the gas phase, and to take into account the moving contact line. Eulerian methods seem to have the potential to solve this modeling. However, the use of the continuous surface force (CSF) model in the volume of fluid (VOF) framework is known to introduce non-physical velocities, called spurious currents. This paper presents an alternative model based on the height function (HF) approach. The use of this method limits spurious currents and makes the VOF methodology suitable for studying Marangoni currents along with the interface of an electrogenerated bubble.

The Chebyshev tau method is examined; a numerical technique which in recent years has been successfully applied to many hydrodynamic stability problems. The orthogonality of Chebyshev functions is used to rewrite the differential equations as a generalized eigenvalue problem. Although a very efficient technique, the occurrence of spurious eigenvalues, which are not always easy to identify, may lead one to believe that a system is unstable when it is not. Thus, the elimination of spurious eigenvalues is of great importance. Boundary conditions are included as rows in the matrices of the generalized eigenvalue problem and these have been observed to be one cause of spurious eigenvalues. Removing boundary condition rows can be difficult. This problem is addressed here, in application to the Bénard convection problem, and to the Orr-Sommerfeld equation which describes parallel flow. The procedure given here can be applied to a wide range of hydrodynamic stability problems.