Related papers: Glimm's Method for Relativistic Hydrodynamics
We present a framework for solving partial different equations on evolving surfaces. Based on the grid-based particle method (GBPM) [18], the method can naturally resample the surface even under large deformation from the motion law. We…
Hydrodynamics simulations are powerful tools for studying fluid behavior under physical forces, enabling extraction of features that reveal key flow characteristics. Traditional post-analysis methods offer high accuracy but incur…
Stochastic gradient descent (SGD) and its variants enable modern artificial intelligence. However, theoretical understanding lags far behind their empirical success. It is widely believed that SGD has a curious ability to avoid sharp local…
Due to computational constraints, running global climate models (GCMs) for many years requires a lower spatial grid resolution (${\gtrsim}50$ km) than is optimal for accurately resolving important physical processes. Such processes are…
The gradient descent (GD) method -- is a fundamental and likely the most popular optimization algorithm in machine learning (ML), with a history traced back to a paper in 1847 (Cauchy, 1847). It was studied under various assumptions,…
We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…
A new consistent, spatially adaptive, smoothed particle hydrodynamics (SPH) method for Fluid-Structure Interactions (FSI) is presented. The method combines several attributes that have not been simultaneously satisfied by other SPH methods.…
Alternating Direction Method of Multipliers (ADMM) has been used successfully in many conventional machine learning applications and is considered to be a useful alternative to Stochastic Gradient Descent (SGD) as a deep learning optimizer.…
Accurate representation of large-scale flow patterns in low-resolution ocean simulations is one of the most challenging problems in ocean modelling. The main difficulty is to correctly reproduce effects of unresolved small scales on the…
Solving partial differential equations (PDEs) on manifolds defined by randomly sampled point clouds is a challenging problem in scientific computing and has broad applications in various fields. In this paper, we develop a two-step…
We consider dry granular flow down an inclined chute with a localised contraction theoretically and numerically. The flow regimes are predicted through a novel extended one-dimensional hydraulic theory. A discrete particle method validated…
In this paper we present a full general relativistic one-dimensional hydro-code which incorporates a modern high-resolution shock-capturing algorithm, with an approximate Riemann solver, for the correct modelling of formation and…
The hydrodynamics of viscoelastic materials (for example polymer melts and solutions) presents interesting and complex phenomena, for example instabilities and turbulent flow at very low Reynolds numbers due to normal stress effects and the…
In conventional fluids, it is well known that Euler-scale equations are plagued by ambiguities and instabilities. Smooth initial conditions may develop shocks, and weak solutions, such as for domain wall initial conditions (the paradigmatic…
Hot, diffuse, relativistic plasmas such as sub-Eddington black hole accretion flows are expected to be collisionless, yet are commonly modeled as a fluid using ideal general relativistic magnetohydrodynamics (GRMHD). Dissipative effects…
We consider the one-dimensional shallow water equations (SW) in a finite channel with variable bottom topography. We pose several initial-boundary-value problems for the SW system, including problems with transparent (characteristic)…
Generalist Anomaly Detection (GAD) aims to train a unified model on an original domain that can detect anomalies in new target domains. Previous GAD methods primarily use only normal samples as references, overlooking the valuable…
We investigate the behavior of the slip length in Newtonian liquids subject to planar shear bounded by substrates with mixed boundary conditions. The upper wall, consisting of a homogenous surface of finite or vanishing slip, moves at a…
We present the second-order multidimensional Staggered Grid Hydrodynamics Residual Distribution (SGH RD) scheme for Lagrangian hydrodynamics. The SGH RD scheme is based on the staggered finite element discretizations as in [Dobrev et al.,…
Flood prediction is critical for emergency planning and response to mitigate human and economic losses. Traditional physics-based hydrodynamic models generate high-resolution flood maps using numerical methods requiring fine-grid…