Related papers: Numerical simulation of rarefied supersonic flows …
We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…
New regulations are imposing noise emissions limitations for the aviation industry which are pushing researchers and engineers to invest efforts in studying the aeroacoustics phenomena. Following this trend, an in-house computational fluid…
A kinetic flux-splitting procedure used in conjunction with local thermodynamic equilibrium in a finite volume allows us to investigate numerically discrete-velocity gas flows. The procedure, outlined for a general discrete-velocity gas, is…
Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth…
This paper is a continuation of our earlier work \cite{NRxx} in which a numerical moment method with arbitrary order of moments was presented. However, the computation may break down during the calculation of the structure of a shock wave…
In this work, we present two numerical methods to approximate solutions of systems of dissipative sine-Gordon equations that arise in the study of one-dimensional, semi-infinite arrays of Josephson junctions coupled through superconducting…
A relativistic version of the rational extended thermodynamics of polyatomic gases based on a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal mode is…
We propose a novel algorithm for the approximation of surface-quasi geostrophic (SQG) flows modeled by a nonlinear partial differential equation coupling transport and fractional diffusion phenomena. The time discretization consists of an…
Designing the sensing architecture for large-scale spatio-temporal systems is hard when accuracy requirements are specified but sensor models are uncertain or unavailable. Classical design treats sensor placement and estimation…
For accurate simulations of rarefied gas flows around moving obstacles, we propose a cut cell method on Cartesian grids: it allows exact conservation and accurate treatment of boundary conditions. Our approach is designed to treat Cartesian…
This review describes recent advances by the authors and others on the topic of incorporating experimental data into molecular simulations through maximum entropy methods. Methods which incorporate experimental data improve accuracy in…
Extreme events play a crucial role in fluid turbulence. Inspired by methods from field theory, these extreme events, their evolution and probability can be computed with help of the instanton formalism as minimizers of a suitable action…
While flow optimization has been extensively studied in the continuum regime, its extension to rarefied gas flows remains less explored. Here, based on the Boltzmann model equation, an adjoint topology optimization method is employed to…
Fluid dynamical simulations are often performed using cheap macroscopic models like the Euler equations. For rarefied gases under near-equilibrium conditions, however, macroscopic models are not sufficiently accurate and a simulation using…
The increasing application of cardiorespiratory simulations for diagnosis and surgical planning necessitates the development of computational methods significantly faster than the current technology. To achieve this objective, we leverage…
The idea of using fast sweeping methods for solving stationary systems of conservation laws has previously been proposed for efficiently computing solutions with sharp shocks. We further develop these methods to allow for a more challenging…
We introduce a theoretical and numerical method to investigate the properties of electro-osmotic flows under conditions of extreme confinement. The present approach, aiming to provide a simple modeling of electrolyte solutions described as…
In this work, we develop an accelerated sharp-interface method based on (Hu et al., JCP, 2006) and (Luo et al., JCP, 2015) for multiphase flows simulations. Traditional multiphase simulation methods use the minimum time step of all fluids…
The present paper deals with the problem of improving the efficiency of large scale turbulent flow simulations. The high-fidelity methods for modelling turbulent flows become available for a wider range of applications thanks to the…
In this work, we explore the method of fundamental solutions (MFS) for solving the regularized 13-moment (R13) equations for rarefied monatomic gases. While previous applications of the MFS in rarefied gas flows relied on problem-specific…