Related papers: Krylov methods for large-scale dynamical systems: …
This book is an extension of my doctoral dissertation, focusing on techniques for analyzing stability (dissipativity) and achieving stabilization of linear systems that are characterized by non-trivial distributed delays. It specifically…
Advanced Krylov subspace methods are investigated for the solution of large sparse linear systems arising from stiff adjoint-based aerodynamic shape optimization problems. A special attention is paid to the flexible inner-outer GMRES…
The Navier-Stokes equations, are understood as the result of the low-order expansion in powers of dimensionless rate of strain $\eta_{ij}=\tau_{0}S_{ij}$, where $\tau_{0}$ is the microscopic relaxation time of a close-to- thermodynamic…
We investigate the dynamics of self-gravitating, spherically-symmetric distributions of fluid through numerical means. In particular, systems involving neutron star models driven far from equilibrium in the strong-field regime of general…
Modeling of fluid flows requires corresponding adequate and effective approaches that would account for multiscale nature of the considered physics. Despite the tremendous growth of computational power in the past decades, modeling of fluid…
In this paper we present a numerical method for hydrodynamic models that arise from time dependent density functional theories of freezing. The models take the form of compressible Navier-Stokes equations whose pressure is determined by the…
Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while…
Simulating the interaction of fluids with immersed moving solids is playing an important role for gaining a better quantitative understanding of how fluid dynamics is altered by the presence of obstacles and which forces are exerted on the…
In the study of gas dynamics, theoretical modeling and numerical simulation are mostly set up with deterministic settings. Given the coarse-grained modeling in theories of fluids, considerable uncertainties may exist between flow-field…
A remarkable feature of fluid dynamics is its relationship with classical dynamics and statistical mechanics. This has motivated in the past mathematical investigations concerning, in a special way, the "derivation" based on kinetic theory,…
Computational fluid dynamics (CFD) simulations are broadly applied in engineering and physics. A standard description of fluid dynamics requires solving the Navier-Stokes (N-S) equations in different flow regimes. However, applications of…
Traditional methods for solving physical equations in curved spaces, especially in fluid mechanics and general relativity, rely heavily on the use of Christoffel symbols. These symbols provide the necessary corrections to account for…
The Rosenbrock-Krylov family of time integration schemes is an extension of Rosenbrock-W methods that employs a specific Krylov based approximation of the linear system solutions arising within each stage of the integrator. This work…
We present a Rvachev function method with the Chebysev collocation for the stability analysis of fluid flow. The strategy is to construct an approximate solution that satisfies all boundary conditions exactly. As an example, we consider the…
In this work, we aimed to replicate and extend the results presented in the DiffFluid paper[1]. The DiffFluid model showed that diffusion models combined with Transformers are capable of predicting fluid dynamics. It uses a denoising…
This paper develops a robust three-level time split high-order Leapfrog/Crank-Nicolson technique for solving the two-dimensional unsteady sobolev and regularized long wave equations arising in fluid mechanics. A deep analysis of the…
A framework is developed based on different uncertainty quantification (UQ) techniques in order to assess validation and verification (V&V) metrics in computational physics problems, in general, and computational fluid dynamics (CFD), in…
In this paper, we obtain the optimal instability threshold of the Couette flow for Navier-Stokes equations with small viscosity $\nu>0$, when the perturbations are in the critical spaces $H^1_xL_y^2$. More precisely, we introduce a new…
This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical…
Recent remarkable progress in computing power and numerical analysis is enabling us to fill a gap in the dynamical systems approach to turbulence. One of the significant advances in this respect has been the numerical discovery of simple…