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Some simulations of Type Ia supernovae feature self-consistent thermonuclear detonations. However, these detonations are not meaningful if the simulations are not resolved, so it is important to establish the requirements for achieving a…

The space-time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell ADER-WENO finite-volume limiting was used for simulation of multidimensional reacting flows with detonation waves. The presented numerical…

One of the main challenges in modeling massive stars to the onset of core collapse is the computational bottleneck of nucleosynthesis during advanced burning stages. The number of isotopes formed requires solving a large set of…

Modeling and simulation of High Power Microwave (HPM) breakdown, a multiscale phenomenon, is computationally expensive and requires solving Maxwell's equations (EM solver) coupled with a plasma continuity equation (plasma solver). In this…

After decades of one-dimensional nucleosynthesis calculations, the growth of computational resources has meanwhile reached a level, which for the first time allows astrophysicists to consider performing routinely realistic multidimensional…

The multi-term time-fractional mixed diffusion-wave equations (TFMDWEs) are considered and the numerical method with its error analysis is presented in this paper. First, a $L2$ approximation is proved with first order accuracy to the…

We present the results of two-dimensional calculations of turbulent nuclear burning of hydrogen-rich material accreted onto a white dwarf of 1 solar mass. The main aim of the present paper is to investigate the question as to whether and…

A method for integrating the chemical equations associated with nuclear combustion at high temperature is presented and extensively checked. Following the idea of E. M\"uller, the feedback between nuclear rates and temperature was taken…

Large-scale simulations of the wave equation in electromagnetism, seismology, and acoustics, can be solved efficiently by finite difference methods. The accuracy of these numerical solutions usually depends on the minimization of…

We present a numerical model which allows us to investigate thermonuclear flames in Type Ia supernova explosions. The model is based on a finite-volume explicit hydrodynamics solver employing PPM. Using the level-set technique combined with…

Direct numerical simulations (DNS) are an indispensable tool for understanding the fundamental physics of turbulent flows. Because of their steep increase in computational cost with Reynolds number ($R_{\lambda}$), well-resolved DNS are…

Large-scale metasurfaces promise nanophotonic performance improvements to macroscopic optics functionality, for applications from imaging to analog computing. Yet the size scale mismatch of centimeter-scale chips versus micron-scale…

With the advent of gravitational wave detectors employing squeezed light, quantum waveform estimation---estimating a time-dependent signal by means of a quantum-mechanical probe---is of increasing importance. As is well known, backaction of…

The large range of time and length scales involved in type Ia supernovae (SN Ia) requires the use of flame models. As a prelude to exploring various options for flame models, we consider, in this paper, high-resolution three-dimensional…

The susceptibility of timestepping algorithms to numerical instabilities is an important consideration when simulating partial differential equations (PDEs). Here we identify and analyze a pernicious numerical instability arising in…

This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma…

Details of the explosion mechanism of core-collapse supernovae (CCSNe) are not yet fully understood. There is an increasing number of numerical examples by ab-initio core-collapse simulations leading to an explosion. Most, if not all, of…

Underwater explosions produce complex fluid phenomena relevant to diverse applications including maritime engineering, medical therapeutics, and inertial confinement fusion. These systems exhibit multiphase flows, chemical kinetics, and…

First results of simulations are presented which compute the dynamical evolution of a Chandrasekhar-mass white dwarf, consisting of equal amounts of carbon and oxygen, from the onset of violent thermonuclear burning, by means of a new…

We investigate thermonuclear explosions within the delayed detonation framework. While spherical delayed detonation models generally reproduce key observational features, a fundamental inconsistency emerges in three dimensions: 3D…