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Solutions to conservation laws satisfy the monotonicity property: the number of local extrema is a non-increasing function of time, and local maximum/minimum values decrease/increase monotonically in time. This paper investigates this…
Computational fluid dynamics and aerodynamics, which complement more expensive empirical approaches, are critical for developing aerospace vehicles. During the past three decades, computational aerodynamics capability has improved…
Designing optimal Bayes filters for nonlinear non-Gaussian systems is a challenging task. The main difficulties are: 1) representing complex beliefs, 2) handling non-Gaussian noise, and 3) marginalizing past states. To address these…
In this paper, we propose a deep learning based reduced order modeling method for stochastic underground flow problems in highly heterogeneous media. We aim to utilize supervised learning to build a reduced surrogate model from the…
We consider the simulation of barotropic flow of gas in long pipes and pipe networks. Based on a Hamiltonian reformulation of the governing system, a fully discrete approximation scheme is proposed using mixed finite elements in space and…
Using the recently developed ``Maximum Entropy'' (or ``least biased'') distribution function to truncate the moment hierarchy arising from kinetic theory, we formulate a far-from-equilibrium macroscopic theory that provides the possibility…
Stokes flows are a type of fluid flow where convective forces are small in comparison with viscous forces, and momentum transport is entirely due to viscous diffusion. Besides being routinely used as benchmark test cases in numerical fluid…
Using quantum Monte Carlo simulations, we investigate the finite-temperature phase diagram of hard-core bosons (XY model) in two- and three-dimensional lattices. To determine the phase boundaries, we perform a finite-size-scaling analysis…
Many entropy-conservative and entropy-stable (summarized as entropy-preserving) methods for hyperbolic conservation laws rely on Tadmor's theory for two-point entropy-preserving numerical fluxes and its higher-order extension via flux…
This work concerns the numerical approximation of a multicomponent compressible Euler system for a fluid mixture in multiple space dimensions on unstructured meshes with a high-order discontinuous Galerkin spectral element method (DGSEM).…
There is growing interest in developing mathematical models and appropriate numerical methods for problems involving networks formed by, essentially, one-dimensional (1D) domains joined by junctions. Examples include hyperbolic equations in…
A hybrid sharp-interface immersed-boundary/front-tracking (IB/FT) method is developed for interface-resolved simulation of evaporating droplets in incompressible multiphase flows. A one-field formulation is used to solve the flow, species…
With growing interest in space exploration, optimized airfoil design has become increasingly important. However, airfoil design in rarefied gas flows remains underexplored because solving the Boltzmann equation formulated in a six…
Max-stable processes are a popular tool for the study of environmental extremes, and the extremal skew-$t$ process is a general model that allows for a flexible extremal dependence structure. For inference on max-stable processes with…
A series of robust and optimal mixed methods based on two mixed formulations of the fourth-order elliptic singular perturbation problem are developed in this paper. First, a mixed method based on a second-order system is proposed without…
Numerical simulation of compressible fluid flows is performed using the Euler equations. They include the scalar advection equation for the density, the vector advection equation for the velocity and a given pressure dependence on the…
The best techniques for the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a variety of concave continuous relaxations of the objective function. A standard…
Three-dimensional (3D) high-speed compressible flow is a typical nonlinear, nonequilibrium, and multiscale complex flow. Traditional fluid mechanics models, based on the quasi-continuum assumption and near-equilibrium approximation, are…
We explore the use of the method of Maximum Entropy (ME) as a technique to generate approximations. In a first use of the ME method the "exact" canonical probability distribution of a fluid is approximated by that of a fluid of hard…
A low-order finite element method is constructed and analysed for an incompressible non-Newtonian flow problem with power-law rheology. The method is based on a continuous piecewise linear approximation of the velocity field and piecewise…