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In three space dimensions, we consider the compressible inviscid model describing the time evolution of two fluids sharing the same velocity and enjoying the algebraic pressure closure. By employing the technique of convex integration, we…
We propose a high order finite difference linear scheme combined with a high order bound preserving maximum-principle-preserving (MPP) flux limiter to solve the incompressible flow system. For such problem with highly oscillatory structure…
In this paper, we present the numerical solution of two-phase flow problems of engineering significance with a space-time finite element method that allows for local temporal refinement. Our basis is the method presented in [3], which…
We present a strategy for solving time-dependent problems on grids with local refinements in time using different time steps in different regions of space. We discuss and analyze two conservative approximations based on finite volume with…
In this paper we design high-order positivity-preserving approximation schemes for an integro-differential model describing photochemical reactions. Specifically, we introduce and analyze three classes of dynamically consistent methods,…
In modeling multivariate time series, it is important to allow time-varying smoothness in the mean and covariance process. In particular, there may be certain time intervals exhibiting rapid changes and others in which changes are slow. If…
This paper introduces a high order numerical framework for efficient and robust simulation of compressible flows. To address the inefficiencies of standard hybridized discontinuous Galerkin (HDG) methods in large scale settings, we develop…
Simulating infiltration in porous media using Richards' equation remains computationally challenging due to its parabolic structure and nonlinear coefficients. While a wide range of numerical methods for differential equations have been…
Godunov type numerical schemes for the class of hyperbolic systems, admitting non-classical $\delta-$ shocks are proposed. It is shown that the numerical approximations converge to the solution and preserve the physical properties of the…
In this paper, we propose a continuous-time primal-dual approach for linearly constrained multiobjective optimization problems. A novel dynamical model, called accelerated multiobjective primal-dual flow, is presented with a second-order…
The spatial discretization of convective terms in compressible flow equations is studied from an abstract viewpoint, for finite-difference methods and finite-volume type formulations with cell-centered numerical fluxes. General conditions…
Numerical methods for hyperbolic conservation laws are needed that efficiently mimic the constraints satisfied by exact solutions, including material conservation and positivity, while also maintaining high-order accuracy and numerical…
Particle methods are less computationally efficient than grid based numerical solution of the Navier Stokes equation. However, they have important advantages including rigorous mass conservation, momentum conservation and isotropy. In…
Multi-component fluid flow simulations in multi-scale porous structures often involve regions that are under-resolved at practical computational resolutions. Accurately capturing the contributions from these unresolved regions is critical.…
This paper presents a parallel and fully conservative adaptive mesh refinement (AMR) implementation of a finite-volume-based kinetic solver for compressible flows. Time-dependent H-type refinement is combined with a two-population…
This paper deals with the early results of a new model of pedestrian flow, conceived within a measure-theoretical framework. The modeling approach consists in a discrete-time Eulerian macroscopic representation of the system via a family of…
The aim of this paper is to present a kinetic numerical scheme for the computations of transient pressurised flows in closed water pipes with variable sections. Firstly, we detail the derivation of the mathematical model in curvilinear…
We propose a novel method for the direct numerical simulation of interfacial flows involving large density contrasts, using a Volume-of-Fluid method. We employ the conservative formulation of the incompressible Navier-Stokes equations for…
Sampling from unnormalized densities presents a fundamental challenge with wide-ranging applications, from posterior inference to molecular dynamics simulations. Continuous flow-based neural samplers offer a promising approach, learning a…
The study of many-body quantum dynamics in strongly-correlated systems is extremely challenging. To date few numerical methods exist which are capable of simulating the non-equilibrium dynamics of two-dimensional quantum systems, in part…