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A second-order $L$-stable exponential time-differencing (ETD) method is developed by combining an ETD scheme with approximating the matrix exponentials by rational functions having real distinct poles (RDP), together with a dimensional…
We present a new numerical method of special relativistic resistive magnetohydrodynamics with scalar resistivity that can treat a range of phenomena, from nonrelativistic to relativistic (shock, contact discontinuity, and Alfv\'en wave).…
In this paper, we present a rigorous proof of the convergence of first order and second order exponential time differencing (ETD) schemes for solving the nonlocal Cahn-Hilliard (NCH) equation. The spatial discretization employs the Fourier…
The paper proposes a novel hybrid method for solving equilibrium problems and fixed point problems. By constructing specially cutting-halfspaces, in this algorithm, only an optimization program is solved at each iteration without the…
2D Total Variation Denoising (TVD) is a widely used technique for image denoising. It is also an important nonparametric regression method for estimating functions with heterogenous smoothness. Recent results have shown the TVD estimator to…
In this work we study arbitrary-order hybrid discretizations of Friedrichs systems. Friedrichs systems provide a framework that goes beyond the standard classification of partial differential equations into hyperbolic or elliptic, and are…
We develop a new dispersion minimizing compact finite difference scheme for the Helmholtz equation in 2 and 3 dimensions. The scheme is based on a newly developed ray theory for difference equations. A discrete Helmholtz operator and a…
Finite difference discretization schemes preserving a subgroup of the maximal Lie invariance group of the one-dimensional linear heat equation are determined. These invariant schemes are constructed using the invariantization procedure for…
Computational fluctuating hydrodynamics aims at understanding the impact of thermal fluctuations on fluid motions at small scales through numerical exploration. These fluctuations are modeled as stochastic flux terms and incorporated into…
A series of third- and fifth-order hybrid compact least-squares central weighted essentially non-oscillatory schemes are proposed and applied to curvilinear structured grids for the finite volume method. In smooth regions, compact…
In this paper, we consider numerical approximations for solving the inductionless magnetohydrodynamic (MHD) equations. By utilizing the scalar auxiliary variable (SAV) approach for dealing with the convective and coupling terms, we propose…
We present in this work a new reconstruction scheme, so-called MUSCL-THINC-BVD scheme, to solve the five-equation model for interfacial two phase flows. This scheme employs the traditional shock capturing MUSCL (Monotone Upstream-centered…
This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. The proposed procedure has several features which distinguishes it from the other procedures for the problem. First of all a sliding…
A comprehensive numerical solution is developed for the transient thermo-elasto-hydrodynamic (TEHD) characteristics of mechanical face seals. Transient lubrication features of the fluid film, transient thermal deformation features of the…
We mimic the conventional explicit Total Variation Diminishing Runge-Kutta (TVDRK) schemes and propose a class of numerical integrators to solve differential equations on a unit sphere. Our approach utilizes the exponential map inherent to…
We present a numerical investigation of stochastic transport in ideal fluids. According to Holm (Proc Roy Soc, 2015) and Cotter et al. (2017), the principles of transformation theory and multi-time homogenisation, respectively, imply a…
We describe a new CSPH-TVD method for numerical integration of hydrodynamical equations. The method is based on combined Lagrange-Euler approaches, and it has been devoted to simulations of hydrodynamical flows in various astrophysical…
A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a…
The context of this work is the development of first order total variation diminishing (TVD) implicit-explicit (IMEX) Runge-Kutta (RK) schemes as a basis of a Multidimensional Optimal Order detection (MOOD) approach to approximate the…
A framework for exponential time discretization of the multilayer rotating shallow water equations is developed in combination with a mimetic discretization in space. The method is based on a combination of existing exponential time…