arXiv subjects
Publications and source records attributed to Madalina Petcu.
We show convergence of a continuous data assimilation method for the Oberbeck-Boussinesq system in the dimension $d=2,3$. Our working hypothesis is boundedness of the reference solution, while the synchronized solution satisfies the equations in a weak sense. The main tool is the relative energy inequality for stochastic problems.
We introduce a simple model of the time evolution of a binary mixture of compressible fluids including the thermal effects. Despite its apparent simplicity, the model is thermodynamically consistent admitting an entropy balance equation. We introduce a suitable weak formulation of the problem based on a combination of the entropy inequality with the total energy conservation principle. Finally, we show compactness of any bounded family of weak solutions and establish a global existence result.
We consider a model of a binary mixture of two immiscible compressible fluids. We propose a numerical scheme and discuss its basic properties: Stability, consistency, convergence. The convergence is established via the method of generalized weak solutions combined with the weak-strong uniqueness principle.
A myth of antiquity is explained with modern science in the context of an ancient naval battle. A legend was invoked by the admiral Pliny the Elder to explain the defeat of Antony and Cleopatra against Octavian at the naval battle of Actium. A fish, called echeneis or remora, is said to have the power to stop ships or to delay their motion by adhering to the hull. Naturalists have since studied how the fish sucking-disk with its typical pattern of parallel striae sticks to its host. Here we show the pattern of the free surface measured in a towing tank in the wake of an ancient galley is similar to the striae pattern of the fish. We have measured the bathymetry at the mouth of the Ambracian Gulf that influenced the physical environment of the battle. The computations demonstrate the increase of wave resistance of a galley as a function of the draft to the water depth ratio in shallow water corresponding to the appearance of a particular wake pattern: the echeneidian free surface pattern.
We consider a model of a two phase flow proposed by Anderson, McFadden and Wheeler taking into account possible thermal fluctuations. The mathematical model consists of the compressible Navier-Stokes system coupled with the Cahn-Hilliard equation, where the latter is driven by a multiplicative temporal white noise accounting for thermal fluctuations. We show that existence of dissipative martingale solutions satisfying the associated total energy balance.
The purpose of this article is to propose ODE based approaches for the numerical evaluation of matrix functions $f(A)$, a question of major interest in the numerical linear algebra. To this end, we model $f(A)$ as the solution at a finite time $T$ of a time dependent equation. We use parallel algorithms, such as the parareal method, on the time interval $[0, T]$ in order to solve the evolution equation obtained. When $f(A)$ is reached as a stable steady state, it can be computed by combining parareal algorithms and optimal control techniques. Numerical illustrations are given.
In this article we consider the inviscid two-dimensional shallow water equations in a rectangle. The flow occurs near a stationary solution in the so called supercritical regime and we establish short term existence of smooth solutions for the corresponding initial and boundary value problem.