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High-resolution spectroscopy has revealed large concentrations of CNO and sometimes other intermediate-mass elements in the shells ejected during nova outbursts, suggesting that the solar composition material transferred from the secondary…
The present research proposes a new memory-efficient method using diffusion models to inject turbulent inflow conditions into Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) for various flow problems. A guided diffusion…
The direct method of construction of local conservation laws of partial differential equations (PDE) is a systematic method applicable to a wide class of PDE systems [Anco S. and Bluman G., Direct construction method for conservation laws…
In this paper, a three-dimensional numerical solver is developed for suspensions of rigid and soft particles and droplets in viscoelastic and elastoviscoplastic (EVP) fluids. The presented algorithm is designed to allow for the first time…
Large eddy simulation (LES) has been increasingly used to tackle vortex-dominated turbulent flows. In LES, the quality of the simulation results hinges upon the quality of the numerical discretizations in both space and time. It is in this…
The adoption of detailed mechanisms for chemical kinetics often poses two types of severe challenges: First, the number of degrees of freedom is large; and second, the dynamics is characterized by widely disparate time scales. As a result,…
Analytical expressions for radial distribution function (RDF) are of critical importance for various applications, such as development of the perturbation theories for equilibrium properties. Theoretically, RDF expressions for…
The numerical simulation of multiphase flows presents several challenges, namely the transport of different phases within de domain and the inclusion of capillary effects. Here, these are approached by enforcing a discrete…
A roughly constant temperature over a wide range of densities is maintained in molecular clouds through radiative heating and cooling. An isothermal equation of state is therefore frequently employed in molecular cloud simulations. However,…
In this visualisation the instantaneous local velocity is expressed in terms of four components to capture the development of and interactions between coherent structures in turbulent flows. It is then possible to isolate the terms linked…
Accurate long-term predictions of large-scale flow features on planets are crucial for understanding global atmospheric and oceanic systems, necessitating the development of numerical methods that can preserve essential physical structures…
Urban flood disaster is one of the most serious natural disasters. Numerous flood simulation models have been proposed and relatively matured. However, two major challenges persist: excessive simplification of the city system and high…
Wildfires represent a problem for ecosystems, human activities, and economies, driven by the climate crisis and land-use changes. Predicting wildfire propagation through mathematical modelling is essential for damage mitigation and risk…
We introduce Lagrangian Flow Networks (LFlows) for modeling fluid densities and velocities continuously in space and time. By construction, the proposed LFlows satisfy the continuity equation, a PDE describing mass conservation in its…
A finite element method for the evolution of a two-phase membrane in a sharp interface formulation is introduced. The evolution equations are given as an $L^2$--gradient flow of an energy involving an elastic bending energy and a line…
We propose an efficient semi-Lagrangian Characteristic Mapping (CM) method for solving the three-dimensional (3D) incompressible Euler equations. This method evolves advected quantities by discretizing the flow map associated with the…
General conservation equations are derived for 2D dense granular flows from the Euler equation within the Boussinesq approximation. In steady flows, the 2D fields of granular temperature, vorticity and stream function are shown to be…
This paper is concerned with probabilistic techniques for forecasting dynamical systems described by partial differential equations (such as, for example, the Navier-Stokes equations). In particular, it is investigating and comparing…
Finite-volume numerical method for study shallow water flows over an arbitrary bed profile in the presence of external force is proposed. This method uses the quasi-two-layer model of hydrodynamic flows over a stepwise boundary with…
To study the dynamics of particles in turbulence when their sizes are comparable to the smallest eddies in the flow, the Kolmogorov length scale, efficient and accurate numerical models for the particle-fluid interaction are still missing.…