The design and implementation of a new framework for adaptive mesh refinement
calculations are described. It is intended primarily for applications in astrophysical fluid …

Strong Stability Preserving Explicit Runge—Kutta Methods | Strong Stability Preserving
Runge-Kutta and Multistep Time Discretizations World Scientific Search This Book Anywhere …

Numerical relativity is central to the investigation of astrophysical sources in the dynamical
and strong-field gravity regime, such as binary black hole and neutron star coalescences …

One of the challenges when simulating astrophysical flows with self-gravity is to compute the
gravitational forces. In contrast to the hyperbolic hydrodynamic equations, the gravity field is …

We develop error-control based time integration algorithms for compressible fluid dynamics
(CFD) applications and show that they are efficient and robust in both the accuracy-limited …

We present a fourth-order accurate finite volume method for the solution of ideal
magnetohydrodynamics (MHD). The numerical method combines high-order quadrature …

Multiderivative time integrators have a long history of development for ordinary differential
equations, and yet to date, only a small subset of these methods have been explored as a …

In this paper, explicit Runge–Kutta (RK) schemes with minimum storage requirements for
systems with very large dimension that arise in the spatial discretization of some partial …

We present a high-order sharp treatment of immersed moving domain boundaries and
material interfaces, and apply it to the advection-diffusion equation in two and three …

We investigate the strong stability preserving (SSP) property of two-step Runge–Kutta
(TSRK) methods. We prove that all SSP TSRK methods belong to a particularly simple …