In this paper, we present a class of parametrized limiters used to achieve strict maximum principle for high order numerical schemes applied hyperbolic conservation laws computation. By decoupling sequence parameters embedded in group explicit inequalities, the fluxes are locally redefined consistent and conservative formulation. We will show that global can be preserved while accuracy underlying scheme is maintained. The less restrictive on CFL number when finite volume scheme. allow...

In this paper, we utilize the maximum-principle-preserving flux limiting technique, originally designed for high-order weighted essentially nonoscillatory (WENO) methods scalar hyperbolic conservation laws, to develop a class of positivity-preserving finite difference WENO ideal magnetohydrodynamic equations. Our scheme, under constrained transport framework, can achieve accuracy, discrete divergence-free condition, and positivity numerical solution simultaneously. Numerical examples in one,...

In this paper, we propose to apply the parametrized maximum-principle-preserving (MPP) flux limiter in [T. Xiong, J.-M. Qiu, and Z. Xu, J. Comput. Phys., 252 (2013), pp. 310--331] discontinuous Galerkin (DG) method for solving convection-diffusion equations. The feasibility of applying proposed MPP limiters is based on fact that cell averages DG solutions are updated a conservative fashion (by using difference). Compared with earlier approach preserving property problems [Y. Zhang, X. C.-W....

We present the functionalized Cahn-Hilliard (FCH) energy, a continuum characterization of interfacial energy whose minimizers describe network morphology solvated polymer membranes. With small set parameters FCH characterizes bilayer, pore-like, and micelle structures. The gradient flows derived from interactions between these structures, including merging pinch-off endcaps formation junctions central to generation morphologies. couple flow model ionic transport which incorporates entropic...

In this paper, we generalize the parametrized maximum principle preserving flux limiting technique, designed for high order WENO method of solving scalar hyperbolic conservation law problems, to convection-dominated diffusion computation. We modify numerical by it toward a lower monotone develop finite difference Runge--Kutta problems. The proposed has several advantages. First, technique can be conveniently applied arbitrarily schemes. It requires only conservative discretization both...

We implement a nonlinear unconditionally gradient stable scheme by Eyre, within the Fourier method framework for long-time numerical integration of Allen-Cahn and Cahn-Hilliard equations, which are flows energy.We propose new iterative procedure to solve scheme.When is applied equation, we show that iteration contractive mapping in L 2 norm large time steps.For establish proposed converges with step constraint.Further, numerically demonstrate steps.The allows spectral accuracy space fast...

Obtaining accurate ultrasonically estimated displacements along both axial (parallel to the acoustic beam) and lateral (perpendicular directions is an important task for various clinical elastography applications (e.g., modulus reconstruction temperature imaging). In this study, a partial differential equation (PDE)–based regularization algorithm was proposed enhance motion tracking accuracy. More specifically, PDE-based algorithm, utilizing two-dimensional (2D) displacement estimates from...

A numerical scheme is presented to solve the nonlinear Helmholtz (NLH) equation modeling second-harmonic generation (SHG) in photonic bandgap material doped with a χ(2) effect and NLH wave propagation Kerr type gratings χ(3) one-dimensional case. Both of these phenomena arise as result combination high electromagnetic mode density reaction from medium. When intensity incident significantly strong, which makes non-negligible, methods based on linearization essentially problem will become...

In this paper, we generalize the technique of anti-diffusive flux corrections for high order finite difference WENO schemes solving conservation laws in [21], to solve Hamilton-Jacobi equations.The objective is obtain sharp resolution kinks, which are derivative discontinuities viscosity solutions equations.We would like resolve kinks better while maintaining accuracy smooth regions.Numerical examples one and two space dimensional problems demonstrate good quality these Hamiltonian corrected...

In this paper, we focus on developing locally conservative high order finite difference methods with provable total variation stability for solving one-dimensional scalar conservation laws. We introduce a new criterion designing schemes by measuring the of an expanded vector. This vector is created from grid values at $t^{n+1}$ and $t^n$ ordering determined upwinding information. Achievable local bounds are obtained to provide sufficient condition not be greater than initial data. apply...

In this paper, we utilize the maximum-principle-preserving flux limiting technique, originally designed for high order weighted essentially non-oscillatory (WENO) methods scalar hyperbolic conservation laws, to develop a class of positivity-preserving finite difference WENO ideal magnetohydrodynamic (MHD) equations. Our schemes, under constrained transport (CT) framework, can achieve accuracy, discrete divergence-free condition and positivity numerical solution simultaneously. Numerical...

We present a self-consistent, dynamic model for the morphology of pore networks which form in Nafion and other ionomer membranes when they imbibe solvent. The incorporates interactions tethered ionic groups with solvent entropic energy counter ions. Numerical simulations are presented display hysteresis, development pearled structures. A framework extensions that couple electrostatic double layer at interface wall transport equations counter-ions is presented. derives generalized Poisson...

In this note, we apply the h-adaptive streamline diffusion finite element method with a small mesh-dependent artificial viscosity to solve nonlinear hyperbolic partial differential equations, objective of achieving high order accuracy and mesh efficiency.We compute numerical solution steady state Burgers equation converging-diverging nozzle problem.The computational results verify that, by suitably choosing coefficient applying adaptive strategy based on posterior error estimate Johnson et...