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We introduce in this contribution the notion of partial Riemann problem. Recall that the Riemann problem describes a shock tube interaction between two given states ; the partial Riemann problem is a generalization of the previous concept…
Variational approaches have been used successfully as a strategy to take advantage from real data measurements. In several applications, this approach gives a means to increase the accuracy of numerical simulations. In the particular case…
We propose a new way to implement Dirichlet boundary conditions for complex shapes using data from a single node only, in the context of the lattice Boltzmann method. The resulting novel method exhibits second-order convergence for the…
Vortices represent a class of topological solitons arising in gauge theories coupled with complex scalar fields, holding significant importance across various domains of modern physics. In this paper we establish the existence of vortex…
Solving numerically hydrodynamical problems of incompressible fluids raises the question of handling first order derivatives (those of pressure) in a closed container and determining its boundary conditions. We research several pressure…
Immersed boundary methods are extensively used for simulations of dynamic solid objects interacting with fluids due to their computational efficiency and modelling flexibility compared to body-fitted grid methods. However, thin geometries,…
Inferring electromagnetic propagation characteristics within the marine atmospheric boundary layer (MABL) from data in real time is crucial for modern maritime navigation and communications. The propagation of electromagnetic waves is well…
We study the exact boundary controllability of a nonlinear coupled system of two Korteweg-de Vries equations on a bounded interval. The model describes the interactions of two weakly nonlinear gravity waves in a stratified fluid. Due to the…
We study a new non-classical class of variational problems that is motivated by some recent research on the non-linear revenue problem in the field of economics. This class of problem can be set up as a maximising problem in the Calculus of…
In this paper, we investigate the incompressible steady Navier-Stokes system with Navier slip boundary condition in a two-dimensional channel. As long as the width of cross-section of the channel grows more slowly than the linear growth,…
Immersed boundary methods for computing confined fluid and plasma flows in complex geometries are reviewed. The mathematical principle of the volume penalization technique is described and simple examples for imposing Dirichlet and Neumann…
This paper presents a general and robust method for the fluid-structure interaction of membranes and shells undergoing large displacement and large added-mass effects by coupling an immersed-boundary method with a shell finite-element…
Stability and boundedness analysis for vector nonlinear systems with variable delays and coefficients remains challenging due to the conservatism of existing methods. Moreover, estimates of the transient behavior of solution norms remain…
The weakly compressible smoothed particle hydrodynamics (WCSPH) method has been employed to simulate various physical phenomena involving fluids and solids. Various methods have been proposed to implement the solid wall, inlet/outlet, and…
A new approach to solving two-point boundary value problems for a wave equation is developed. This new approach exploits the principle of stationary action to reformulate and solve such problems in the framework of optimal control. In…
The diffuse domain method for partial differential equations on complicated geometries recently received strong attention in particular from practitioners, but many fundamental issues in the analysis are still widely open. In this paper we…
This paper deals with some classes of Kirchhoff type problems on a double phase setting and with nonlinear boundary conditions. Under general assumptions, we provide multiplicity results for such problems in the case when the perturbations…
Boundary value problems for second-order elliptic equations in divergence form, whose nonlinearity is governed by a convex function of non-necessarily power type, are considered. The global boundedness of their solutions is established…
The complicated dynamics of the contact line of a moving droplet on a solid substrate often hamper the efficient modeling of microfluidic systems. In particular, the selection of the effective boundary conditions, specifying the contact…
This work considers a Motion Planning Problem with Dynamic Obstacles (MPDO) in 2D that requires finding a minimum-arrival-time collision-free trajectory for a point robot between its start and goal locations amid dynamic obstacles moving…