In this paper, we focus on the application and illustration of the approach developed in part I. This approach is found to be useful in the construction of stable and monotone central difference schemes for hyperbolic systems. A new modification of the central Lax–Friedrichs scheme is developed to be of second-order accuracy. The stability of several versions of the developed central scheme is ...

The Courant-Friedrichs-Lewy (CFL) condition guarantees the stability of the popular explicit leapfrog method for the wave equation. However, it limits the choice of the time step size to be bounded by the minimal mesh size in the spatial finite element mesh. This essentially prohibits any sort of adaptive mesh refinement that would be required to reveal optimal convergence rates on domains with...

A dissipation theory is proposed for the potentials-based FDTD algorithm case of inhomogeneous lossless media. We show that under Courant-Friedrichs-Lewy (CFL) limit, equations describing time evolution scalar and vector potentials can be seen as a system. The developed provides insights into how electromagnetic energy power flow are approximated in schemes. It also used to create new algorithm...

We develop error-control based time integration algorithms for compressible fluid dynamics (CFD) applications and show that they are efficient robust in both the accuracy-limited stability-limited regime. Focusing on discontinuous spectral element semidiscretizations, we design new controllers existing methods some embedded Runge-Kutta pairs. demonstrate importance of choosing adequate controll...

This paper presents a Godunov-type large time step (LTS) solver of the non-homogeneous shallow water equations (SWEs). Source terms are decomposed into simple characteristic waves in approximate Riemann solvers (ARS) and exact (ERS), information is transferred over multiple cells per using LTS method. Benchmark simulations presented different solution algorithms (ARS ERS with without entropy fi...

A simulation model of the human body is developed in frequency dependent Crank Nicolson finite difference time domain (FD-CN-FDTD) method. Numerical simulation of electromagnetic wave propagation inside the human head is presented. Advantages of using time discretization beyond the Courant Friedrich-Lewy (CFL) limit in FD-CN-FDTD method are shown. Parallelization using Open Multi-Processing (Op...

The maximum time step size for the explicit finite-difference scheme complies with Courant–Friedrichs–Lewy (CFL) stability condition, which essentially restricts optimization and tuning of communication-intensive massive seismic wave simulation in a parallel manner. This study brings forward model-order reduction (MOR) method to simulate acoustic propagation. It briefly takes advantage update m...

A semi-Lagrangian scheme is applied for the first time to computations of charged particle motions along magnetic field lines, to numerically solve the δf gyrokinetic equations in a flux tube geometry. This new solver adopted in the gyrokinetic Vlasov simulations has an advantage over the conventional Eulerian codes in calculating the parallel dynamics, because semi-Lagrangian schemes are free ...

Three-dimensional configurations of helical plasmas bring numerical difficulties to gyrokinetic simulations of plasma turbulent transport in toroidal fusion devices. Watanabe et al. have investigated the ion-temperature-gradient (ITG)-driven turbulence in helical plasmas by means of the gyrokinetic Vlasov simulation code GVK [1]. Because of a large number of grid points along a magnetic field l...