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We develop two new sets of stable, rank-adaptive Dynamically Orthogonal Runge-Kutta (DORK) schemes that capture the high-order curvature of the nonlinear low-rank manifold. The DORK schemes asymptotically approximate the truncated singular…
We use SPH simulations to investigate the gravitational fragmentation of expanding shells through the linear and non--linear regimes. The results are analysed using spherical harmonic decomposition to capture the initiation of structure…
We aim to study the influence of radiative cooling on the standing kink oscillations of a coronal loop. Using the FLASH code, we solved the 3D ideal magnetohydrodynamic equations. Our model consists of a straight, density enhanced and…
A new approach for the reduction of tensor integrals is described. The standard decomposition \`{a} la Davydychev is applied. Integrals with higher indices are then expressed in terms of scalar higher-dimensional integrals with generic…
This paper puts forth two new closure models for the proper orthogonal decomposition reduced-order modeling of structurally dominated turbulent flows: the dynamic subgrid-scale model and the variational multiscale model. These models, which…
Kink oscillations are frequently observed in coronal loops. This work aims to numerically clarify the influence of loop curvature on horizontally and vertically polarized kink oscillations. Working within the framework of ideal MHD, we…
Transverse oscillations of thin threads in solar prominences are frequently reported in high-resolution observations. Two typical features of the observations are that the oscillations are damped in time and that simultaneous mass flows…
We study the behavior of cylindrical objects as they sink into a drygranular bed fluidized due to lateral oscillations. Somewhat unexpectedly, we have found that, within a large range of lateral shaking powers,cylinders with flat bottoms…
Solving compressible flows containing discontinuities remains a major challenge for numerical methods especially on unstructured grids. Thus in this work, we make contributions to shock capturing schemes on unstructured grids with aim of…
We simulate the sintering of particle aggregates due to surface diffusion. As a method we use Kinetic Monte-Carlo simulations in which elasticity can explicitly be taken into account. Therefore it is possible to investigate the shape…
The Strait of Gibraltar is a region characterized by intricate oceanic sub-mesoscale features, influenced by topography, tidal forces, instabilities, and nonlinear hydraulic processes, all governed by the nonlinear equations of fluid…
A Monte Carlo model was used to study the scattering error of an absorption meter with a divergent light beam and a limited acceptance angle of the receiver. Reflections at both ends of the tube were taken into account. Calculations of the…
This paper investigates a class of algorithms for numerical integration of a function in d dimensions over a compact domain by Monte Carlo methods. We construct a histogram approximation to the function using a partition of the integration…
We investigate the use of conformal maps for the acceleration of convergence of the trapezoidal rule and Sinc numerical methods. The conformal map is a polynomial adjustment to the $\sinh$ map, and allows the treatment of a finite number of…
We consider the computational efficiency of Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) methods applied to partial differential equations with random coefficients. These arise, for example, in groundwater flow modelling, where a…
Displacement estimation in optical coherence tomography (OCT) imaging is relevant for several potential applications, e.g. for optical coherence elastography (OCE) for corneal biomechanical characterization. Larger displacements may be…
We introduce an algorithm for treating growth on surfaces which combines important features of continuum methods (such as the level-set method) and Kinetic Monte Carlo (KMC) simulations. We treat the motion of adatoms in continuum theory,…
A computational approach has been developed for the analysis of the properties of 3D dislocation substructures generated by the vector density continuum dislocation dynamics (CDD), within the framework of crystal plasticity. In the CDD…
The error scaling for Markov-Chain Monte Carlo techniques (MCMC) with $N$ samples behaves like $1/\sqrt{N}$. This scaling makes it often very time intensive to reduce the error of computed observables, in particular for applications in…
In a previous paper we showed that, like the migration speed, the eccentricity damping efficiency is modulated linearly by the depth of the partial gap a planet carves in the disk surface density profile, resulting in less efficient…