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Data-driven methods for modelling purposes in fluid mechanics are a promising alternative given the continuous increase of both computational power and data-storage capabilities. Highly non-linear flows including turbulence and reaction are…
The present work focuses on the numerical approximation of the weak solutions of the shallow water model over a non-flat topography. In particular, we pay close attention to steady solutions with nonzero velocity. The goal of this work is…
A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…
In this paper we consider the problem of analytical continuation of solutions to the system of thermoelasticity in a bounded domain from their values and values of their strains on a part of the boundary of this domain, i.e., the Cauchy…
In this numerical study, an original approach to simulate non-isothermal viscoelastic fluid flows at high Weissenberg numbers is presented. Stable computations over a wide range of Weissenberg numbers are assured by using the root…
Due to the limited cell resolution in the representation of flow variables, a piecewise continuous initial reconstruction with discontinuous jump at a cell interface is usually used in modern computational fluid dynamics methods. Starting…
The numerical simulation of fluid flow through a complex geometry with heat transfer is of strong interest for many applications, such as oil-filled power transformers. A fundamental challenge here is that high resolution is necessary to…
In this paper, we perform a numerical analysis in frequency domain for various electromagnetic problems based on discrete exterior calculus (DEC) with an arbitrary 2-D triangular or 3-D tetrahedral mesh. We formulate the governing equations…
We study numerically the standard one pressure model of two fluid flows with energy equations. This system is not solved in time derivative. It has been transformed into an equivalent system solved in time derivative. We show that the…
This article introduces a novel numerical approach, based on Finite Volume Techniques, for studying fully nonlinear coagulation-fragmentation models, where both the coagulation and fragmentation components of the collision operator are…
Shallow flows are common in natural and human-made environments. Even for simple rectangular shallow reservoirs, recent laboratory experiments show that the developing flow fields are particularly complex, involving large-scale turbulent…
Numerical simulation of compressible fluid flows is performed using the Euler equations. They include the scalar advection equation for the density, the vector advection equation for the velocity and a given pressure dependence on the…
Direct numerical simulation of threedimensional chaotic motion of a dielectric liquid with a free surface under the action of external horizontal electric field is carried out. The numerical model takes into account the effects of surface…
A closure model is presented for large-eddy simulation (LES) based on the three-dimensional variational data assimilation algorithm. The approach aims at reconstructing high-fidelity kinetic energy spectra in coarse numerical simulations by…
In this paper, we rigorously investigate the truncation method for the Cauchy problem of Helmholtz equations which is widely used to model propagation phenomena in physical applications. The method is a well-known approach to the…
The paper develops a method for the numerical simulation of a free-surface flow of incompressible viscous fluid around a streamlined body. The body is a rigid stationary construction partially submerged in the fluid. The application we are…
We prove that both local and non-local formulations of the Degasperis-Procesi equation possess a pseudospherical nature. As a result, solutions determined by Cauchy problems with non-trivial initial data and a minimal specific regularity…
We systematically validate the static local mesh refinement capabilities of a recently proposed IMEX-DG scheme implemented in the framework of the deal.II library. Non-conforming meshes are employed in atmospheric flow simulations to…
We live in an age in which high-performance computing is transforming the way we do science. Previously intractable problems are now becoming accessible by means of increasingly realistic numerical simulations. One of the most enduring and…
The propagation of cracks driven by a pressurized fluid emerges in several areas of engineering, including structural, geotechnical, and petroleum engineering. We present a robust numerical framework to simulate fluid-driven fracture…