Multi-dimensional fluid flow plays a paramount role in the explosions of massive stars as
core-collapse supernovae. In recent years, three-dimensional (3D) simulations of these …

A latitude–longitude grid is used by almost all operational atmospheric forecast models, and
many research models. However, it is expected that the advantages of a latitude–longitude …

In this article we survey r-adaptive (or moving grid) methods for solving time-dependent
partial differential equations (PDEs). Although these methods have received much less …

Efficient simulation of plasmas in various contexts often involves the use of meshes that
conform to the intrinsic geometry of the system under consideration. We present here a …

Context. Recent, nonlinear simulations of wave generation and propagation in full-star
models have been carried out in the anelastic approximation using spectral methods …

We present an approach for constructing finite-volume methods for flux-divergence forms to
any order of accuracy defined as the image of a smooth mapping from a rectangular …

We apply the tensor train (TT) decomposition to construct the tensor product polynomial
chaos expansion (PCE) of a random field, to solve the stochastic elliptic diffusion PDE with …

The cores of main sequence intermediate-and high-mass stars are convective. Mixing at the
radiative–convective boundary, waves excited by the convection, and magnetic fields …

Development of scientific software involves tradeoffs between ease of use, generality, and
performance. We describe the design of a general hyperbolic PDE solver that can be …

We present an algorithm for the numerical simulation of seismic wave propagation in models
with a complex near surface part and free surface topography. The approach is based on the …