Related papers: A non column based fully unstructured implementati…

Accurate and high-resolution Earth system model (ESM) simulations are essential to assess the ecological and socio-economic impacts of anthropogenic climate change, but are computationally too expensive to be run at sufficiently high…

We use a novel parameterization of the flowing Hamiltonian to show that the flow equations based on continuous unitary transformations, as proposed by Wegner, can be implemented through a nonlinear partial differential equation involving…

In the spirit of minimal modeling of complex systems, we develop an idealized two-column model to investigate the climate of tidally locked terrestrial planets with Earth-like atmospheres in the habitable zone of M-dwarf stars. The model is…

Deep neural networks have made great achievements in rainfall prediction.However, the current forecasting methods have certain limitations, such as with blurry generated images and incorrect spatial positions. To overcome these challenges,…

We show that for the simulation of crack propagation in quasi-brittle, two-dimensional solids, very good results can be obtained with an embedded strong discontinuity quadrilateral finite element that has incompatible modes. Even more…

We present a discontinuous finite element method for the shallow water equations which exploits high-resolution realistic bathymetry data without any regularity assumption, also in the case of high-order discretizations. We prove a number…

Next-generation galaxy surveys promise unprecedented precision in testing gravity at cosmological scales. However, realising this potential requires accurately modelling the non-linear cosmic web. We address this challenge by exploring…

In many practical applications, evaluating the joint impact of combinations of environmental variables is important for risk management and structural design analysis. When such variables are considered simultaneously, non-stationarity can…

Physics-based numerical models have been the bedrock of atmospheric sciences for decades, offering robust solutions but often at the cost of significant computational resources. Deep learning (DL) models have emerged as powerful tools in…

We develop a novel data-driven approach to modeling the atmospheric boundary layer. This approach leads to a nonlocal, anisotropic synthetic turbulence model which we refer to as the deep rapid distortion (DRD) model. Our approach relies on…

Downscaling is necessary to generate high-resolution observation data to validate the climate model forecast or monitor rainfall at the micro-regional level operationally. Dynamical and statistical downscaling models are often used to get…

Context. Acoustic waves in the Sun are affected by the atmospheric layers, but this region is often ignored in forward models due to the increase in computational cost. Aims. The purpose of this work is to take into account the solar…

We propose a new numerical method to solve the Cahn-Hilliard equation coupled with non-linear wetting boundary conditions. We show that the method is mass-conservative and that the discrete solution satisfies a discrete energy law similar…

In this work, we present a novel nonlocal nonlinear coarse grid approximation using a machine learning algorithm. We consider unsaturated and two-phase flow problems in heterogeneous and fractured porous media, where mathematical models are…

Climate change is causing the intensification of rainfall extremes. Precipitation projections with high spatial resolution are important for society to prepare for these changes, e.g. to model flooding impacts. Physics-based simulations for…

This paper deals with the spectral element modeling of seismic wave propagation at the global scale. Two aspects relevant to low-frequency studies are particularly emphasized. First, the method is generalized beyond the Cowling…

We present a finite element discretization of a non-linear diffusion equation used in the field of critical phenomena and, more recently, in the context of Dynamic Density Functional Theory. The discretized equation preserves the structure…

Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection-diffusion partial differential equation provides a…

We describe a numerical model for the interaction of light with large raindrops using realistic nonspherical drop shapes. We apply geometrical optics and a Monte Carlo technique to perform ray traces through the drops. We solve the problem…

We introduce a novel diffusion-based spectral algorithm to tackle regression analysis on high-dimensional data, particularly data embedded within lower-dimensional manifolds. Traditional spectral algorithms often fall short in such…