相关论文: A positivity-preserving Eulerian two-phase approac…

Numerical simulations of compressible real-fluid flows are notoriously plagued by spurious pressure oscillations arising in regions of abrupt flow variations. As a possible remedy, several numerical formulations enforce the pressure…

An important component of a number of computational modeling algorithms is an interpolation method that preserves the positivity of the function being interpolated. This report describes the numerical testing of a new positivity-preserving…

Over short time intervals planetary ephemerides have been traditionally represented in analytical form as finite sums of periodic terms or sums of Poisson terms that are periodic terms with polynomial amplitudes. Nevertheless, this…

The stochastic logistic model with regime switching is an important model in the ecosystem. While analytic solution to this model is positive, current numerical methods are unable to preserve such boundaries in the approximation. So,…

In this work, we present the construction of two distinct finite element approaches to solve the Porous Medium Equation (PME). In the first approach, we transform the PME to a log-density variable formulation and construct a continuous…

Robust estimation is essential in computer vision, robotics, and navigation, aiming to minimize the impact of outlier measurements for improved accuracy. We present a fast algorithm for Geman-McClure robust estimation, FracGM, leveraging…

We develop a new finite volume method using unstructured mesh-vertex grids for coupled systems modeling shallow water flows and solute transport over complex bottom topography. Novel well-balanced positivity preserving discretization…

We propose and analyze a first-order finite difference scheme for the functionalized Cahn-Hilliard (FCH) equation with a logarithmic Flory-Huggins potential. The semi-implicit numerical scheme is designed based on a suitable convex-concave…

A kinetic model with flexible velocities is presented for solving the multi-component Euler equations. The model employs a two-velocity formulation in 1D and a three-velocity formulation in 2D. In 2D, the velocities are aligned with the…

In this manuscript we present a novel and efficient numerical method for the compressible viscous and resistive MHD equations for all Mach number regimes. The time-integration strategy is a semi-implicit splitting, combined with a hybrid…

In this paper, we propose a class of explicit positivity preserving numerical methods for general stochastic differential equations which have positive solutions. Namely, all the numerical solutions are positive. Under some reasonable…

This work focuses on the formulation of a four-equation model for simulating unsteady two-phase mixtures with phase transition and strong discontinuities. The main assumption consists in a homogeneous temperature, pressure and velocity…

In this paper, Hamiltonian and energy preserving reduced-order models are developed for the rotating thermal shallow water equation (RTSWE) in the non-canonical Hamiltonian form with the state-dependent Poisson matrix. The high fidelity…

In this work, we propose an efficient and robust multigrid method for solving the time-fractional heat equation. Due to the nonlocal property of fractional differential operators, numerical methods usually generate systems of equations for…

A two-phase, low-Mach-number flow solver is created and verified for variable-density liquid and gas with phase change. The interface is sharply captured using a split Volume-of-Fluid method generalized for a non-divergence-free liquid…

We present a novel positive kinetic scheme built on the efficient collide-and-stream algorithm of the lattice Boltzmann method (LBM) to address hyperbolic conservation laws. We focus on the compressible Euler equations with strong…

This paper introduces a family of entropy-conserving finite-difference discretizations for the compressible flow equations. In addition to conserving the primary quantities of mass, momentum, and total energy, the methods also preserve…

Assumed having axial symmetry, the streamer discharge is often described by a fluid model in cylindrical coordinate system, which consists of convection dominated (diffusion) equations with source terms, coupled with a Poisson's equation.…

High order algorithms have emerged in numerical astrophysics as a promising avenue to reduce truncation error (proportional to a power of the linear resolution $\Delta x$) with only a moderate increase to computational expense. Significant…

We consider three types of subdiffusion models, namely single-term, multi-term and distributed order fractional diffusion equations, for which the maximum-principle holds and which, in particular, preserve nonnegativity. Hence the solution…