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In this study we have developed a flexible and efficient numerical scheme for the simulation of three-dimensional incompressible flows in spherical coordinates. The main idea, inspired by a similar strategy as (Verzicco, R., Orlandi, P.,…
For the two-layer shallow water equations, a high-order compact gas-kinetic scheme (GKS) on triangular mesh is proposed. The two-layer shallow water equations have complex source terms in comparison with the single layer equations. The main…
We present a method to simulate nonhydrostatic ocean flows on a horizontally-unstructured grid with a moving generalized vertical coordinate (GVC). The nonhydrostatic governing equations are transformed to a GVC system that can represent…
Conventional mathematical models for simulating incompressible fluid flow problems are based on the Navier-Stokes equations expressed in terms of pressure and velocity. In this context, pressure-velocity coupling is a key issue, and…
A finite difference upwind discretization scheme in two dimensions is presented in detail for the transient simulation of the highly coupled non-linear partial differential equations of the full hydrodynamic model, providing thereby a…
Waves are all around us--be it in the form of sound, electromagnetic radiation, water waves, or earthquakes. Their study is an important basic tool across engineering and science disciplines. Every wave solver serving the computational…
In the paper we discuss the main features of the software package for numerical simulations of the surface water dynamics. We consider an approximation of the shallow water equations together with the parallel technologies for NVIDIA CUDA…
Turbulent dynamics in the scrape-off layer (SOL) of magnetic fusion devices is intermittent with large fluctuations in density and pressure. Therefore, a model is required that allows perturbations of similar or even larger magnitude to the…
The gravimetry measurements from the Gravity Recovery and Climate Experiment (GRACE) and its follow-on (GRACE-FO) satellite mission provide an essential way to monitor changes in ocean bottom pressure ($p_b$), which is a critical variable…
Granular flow problems characterized by large deformations are widespread in various applications, including coastal and geotechnical engineering. The paper deals with the application of a rigid-perfectly plastic two-phase model extended by…
In the present manuscript, we consider the problem of dispersive wave simulation on a rotating globally spherical geometry. In this Part IV, we focus on numerical aspects while the model derivation was described in Part III. The algorithm…
Accurate modeling of sea ice dynamics is critical for predicting environmental variables and is important in applications such as navigating ice breaker ships. Research for both modeling and simulating sea ice dynamics is ongoing, with the…
Numerical simulations of flows are required for numerous applications, and are usually carried out using shallow water equations. We describe the FullSWOF software which is based on up-to-date finite volume methods and well-balanced schemes…
The volume of fluid (VOF) method is increasingly used in computational fluid dynamics (CFD) simulations of turbulent two-phase flows. The Reynolds-Averaged Navier-Stokes (RANS) approach is an economic and practical way for turbulent VOF…
Non-orthogonality errors in unstructured Finite Volume methods for simulating incompressible two-phase flows may break the force-balanced discretization. We show that applying the same explicit non-orthogonality correction for all gradient…
Direct numerical simulation (DNS) of turbulent flows is computationally expensive and cannot be applied to flows with large Reynolds numbers. Large eddy simulation (LES) is an alternative that is computationally less demanding, but is…
Accurate representation of vertical turbulent fluxes is crucial for numerical ocean modelling, both in global and coastal applications. The state-of-the-art approach is to use two-equation turbulence closure models which introduces two…
Fluid simulation is an important research topic in computer graphics (CG) and animation in video games. Traditional methods based on Navier-Stokes equations are computationally expensive. In this paper, we treat fluid motion as point cloud…
Hydrodynamic simulations have become irreplaceable in modern cosmology for exploring complex systems and making predictions to steer future observations. In Chapter 1, we begin with a philosophical discussion on the role of simulations in…
The computational complexity of simulating seismic waves demands continual exploration of more efficient numerical methods. While Finite Volume methods are widely acclaimed for tackling general nonlinear hyperbolic (wave) problems, their…