Performance study of the multiwavelet discontinuous Galerkin approach for solving the Green‐Naghdi equations

This paper presents a multiresolution discontinuous Galerkin scheme for the adaptive solution of Boussinesq‐type equations. The model combines multiwavelet‐based grid adaptation with a discontinuous Galerkin (DG) solver based on the system of fully nonlinear and weakly dispersive Green‐Naghdi (GN) equations. The key feature of the adaptation procedure is to conduct a multiresolution analysis using multiwavelets on a hierarchy of nested grids to improve the efficiency of the reference DG scheme on a uniform grid by computing on a locally refined adapted grid. This way the local resolution level will be determined by manipulating multiwavelet coefficients controlled by a single user‐defined threshold value. The proposed adaptive multiwavelet discontinuous Galerkin solver for GN equations (MWDG‐GN) is assessed using several benchmark problems related to wave propagation and transformation in nearshore areas. The numerical results demonstrate that the proposed scheme retains the accuracy of the reference scheme, while significantly reducing the computational cost

A discontinuous Galerkin method for a new class of Green-Naghdi equations on simplicial unstructured meshes

In this paper, we introduce a discontinuous Finite Element formulation on simplicial unstructured meshes for the study of free surface flows based on the fully nonlinear and weakly dispersive Green-Naghdi equations. Working with a new class of asymptotically equivalent equations, which have a simplified analytical structure, we consider a decoupling strategy: we approximate the solutions of the classical shallow water equations supplemented with a source term globally accounting for the non-hydrostatic effects and we show that this source term can be computed through the resolution of scalar elliptic second-order sub-problems. The assets of the proposed discrete formulation are: (i) the handling of arbitrary unstructured simplicial meshes, (ii) an arbitrary order of approximation in space, (iii) the exact preservation of the motionless steady states, (iv) the preservation of the water height positivity, (v) a simple way to enhance any numerical code based on the nonlinear shallow water equations. The resulting numerical model is validated through several benchmarks involving nonlinear wave transformations and run-up over complex topographies

Adaptive mesh refinement method. Part 2: Application to tsunamis propagation

Numerical simulations of multi dimensional large scale fluid-flows such as tsunamis, are still nowadays a challenging and a difficult problem. To this purpose, a parallel finite volume scheme on adaptive unstructured meshes for multi dimensional Saint-Venant system is presented. The adaptive mesh refinement method is based on a block-based decomposition (called BB-AMR) which allows quick meshing and easy parallelization. The main difficulty addressed here concerns the selection of the mesh refinement threshold which is certainly the most important parameter in the AMR method. Usually, the threshold is calibrated according to the test problem to balance the accuracy of the solution and the computational cost. To avoid " hand calibration " , we apply an automatic threshold method based on the decreasing rearrangement function of the mesh refinement criterion. This method is applied and validated successfully to the one and two dimensional non homogeneous Saint-Venant system through several tsunamis propagation test cases

Breakup of Liquid Feedstock in Plasma Spraying

Suspension plasma spray is an emerging technology to produce functional nanostructured coatings at moderate cost. In general, in this technique, the liquid is injected radially into a high-velocity high-temperature plasma flow. After liquid breakup and evaporation, solid particles remain in the field and impact the substrate. Preliminary studies have shown that liquid jet atomization is the primary phenomenon that controls the coating quality. However, due to the complex thermophysical properties of plasma and its intricate flow physics, the breakup processes of liquid jets in plasma crossflows have not been investigated comprehensively yet. In general, the gaseous Reynolds number and the liquid-to-gas density ratio in this process are around 50 and 10,000, respectively, which are far outside the limits commonly observed in engines and wind tunnels. In this regard, detailed features of the breakup phenomena of the liquid jets injected in plasma and air crossflow are provided. Moreover, a case study has been established to analyze the effect of changing the surface tension of the liquid in the plasma spray process. The finite volume scheme is used to solve the incompressible variable-density Navier-Stokes equations. In addition, the volume of fluid (VOF) approach is utilized to track the gas-liquid interfaces. Finally, qualitative results such as instantaneous snapshots and shape of the liquid jet cross-sections, in company with quantitative data like including fracture point location, length of surface waves and size of the droplets have been presented

Model Skill and Sensitivity for Simulating Wave Processes on Coral Reefs Using a Shock-Capturing Green-Naghdi Solver

International audienceWave flume data from published benchmark experiments were used to extensively evaluate numerical model skill and sensitivity for applying a shock-capturing Green-Naghdi (GN) model to simulate nonlinear wave transformation processes on complex coral reefs. Boussinesq-type models that utilise nonlinear shallow water equations (NSWEs) to represent wave breaking and dissipation hold significant potential for understanding coastal hazards associated with global environmental change and sea-level rise. These fully nonlinear phase-resolving models typically require a threshold condition to switch from dispersive equations to shock-capturing NSWEs in areas of active wave breaking. However, limited information exits regarding how this splitting approach influences the behaviour of different surf-zone processes that contribute to wave runup and inundation on coral reefs. This paper presents a comprehensive analysis of model sensitivity to explore how input parameters that control wave breaking and dissipation influence the behaviour of sea-swell (SS) waves, infragravity (IG) waves, wave setup, runup and solitary waves on coral reefs. Results show that each wave process exhibits unique sensitivity to the free-surface slope threshold (B) that is used to represent areas of active wave breaking by locally switching from the weakly-dispersive GN equations to the shock-capturing NSWEs. However, accurate representation of all wave processes can be achieved if the wave-face steepens to at least 35 degrees (B ≥ 0.7) before breaking is initiated. Results from this research support and encourage the use of nonlinear phase-resolving wave models as tools for academic research, coastal management, coastal engineering and hazard forecasting on atoll and fringing reef environments

Numerical and experimental analyses of a solid impacting a water surface

To date, water-impact events remain an unsolved problem from both a mathematical and a numerical point of view. Complex hydrodynamic phe- nomena are involved in the study of this problem. Several authors have at- tempted to describe these phenomena analytically and numerically, but a general model remains yet unclear. Nowadays, e↵orts are concentrated on the fluid-structure interaction (FSI), as this influences the results dramat- ically. Recent advances on FSI indicate that several challenges arise from high-fidelity fully-coupled water-impact problems, where both global and local phenomena cannot be reproduced accurately at the same time. This projects proposes a simple yet promising approach to model the fluid domain within the fluid-structure interaction of the problem. The dimensionless Navier-Stokes equations for the case of an incompressible variable-density flow are solved by means of the open-source software Basilisk. Numerical simulations are compared with experiments, yielding noteworthy results. The main charac- teristics of the flow gathered in experimental observations were reproduced numerically, with a higher degree of accuracy in some cases than in others. Still, improvements must be made before adopting this methodology for ver- tical impacts or ditching events. Particularly, the approach used to impose the boundary condition on the solid must be revised and possibly discarded. If that were the case, the embedded boundaries technique would be a strong candidate. Furthermore, additional sources in the convergence of results, such as surface tension or bubbles-droplets removal, could be subjected to analysis.Ingeniería Aeroespacia