Related papers: Adaptively Implicit Advection for Atmospheric Flow…
A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermodynamically consistent diffuse interface model is presented. The scheme is consistent in the sense that it allows for a discrete in time…
We propose a new method that extends conservative explicit multirate methods to implicit explicit-multirate methods. We develop extensions of order one and two with different stability properties on the implicit side. The method is suitable…
For simulating incompressible flows by projection methods. it is generally accepted that the pressure-correction stage is the most time-consuming part of the flow solver. The objective of the present work is to develop a fast hybrid…
A semi-implicit, residual-based variational multiscale (VMS) formulation is developed for the incompressible Navier--Stokes equations. The approach linearizes convection using an extrapolated (Oseen-type) convecting velocity, producing a…
High-order implicit shock tracking (fitting) is a class of high-order, optimization-based numerical methods to approximate solutions of conservation laws with non-smooth features by aligning elements of the computational mesh with…
Machine-learned surrogate modeling of advection may accelerate geoscientific models, but existing approaches have either achieved limited speedup or have sacrificed spatial resolution compared to the model they are trained to emulate. We…
In this study, a novel semi-implicit second-order temporal scheme combined with the finite element method for space discretization is proposed to solve the coupled system of infiltration and solute transport in unsaturated porous media. The…
A novel second order family of explicit stabilized Runge-Kutta-Chebyshev methods for advection-diffusion-reaction equations is introduced. The new methods outperform existing schemes for relatively high Peclet number due to their favorable…
Implicit solvers present strong limitations when used on supercomputing facilities and in particular for adaptive mesh-refinement codes. We present a new method for implicit adaptive time-stepping on adaptive mesh refinement-grids. We…
We develop numerical schemes for solving the isothermal compressible and incompressible equations of fluctuating hydrodynamics on a grid with staggered momenta. We develop a second-order accurate spatial discretization of the diffusive,…
We consider high order, implicit Runge-Kutta schemes to solve time-dependent stiff PDEs on dynamically adapted grids generated by multiresolution analysis for unsteady problems disclosing localized fronts. The multiresolution finite volume…
The advection-diffusion equation is studied via a global Lagrangian coordinate transformation. The metric tensor of the Lagrangian coordinates couples the dynamical system theory rigorously into the solution of this class of partial…
Advection-diffusion problems of magnetic field and tracer field are analyzed using the field theoretic perturbative renormalization group. Both advected fields are considered to be passive, i.e., without any influence on the turbulent…
In this paper, we introduce a fourth-order accurate finite element method for incompressible variable density flow. The method is implicit in time and constructed with the Taylor series technique, and uses standard high-order Lagrange basis…
We show the impact that scalar structures deformation and mixing has on the fate of plumes of waterborne contaminant transported through a chemically heterogeneous, partially adsorbing porous medium. Via pore-scale simulations, we follow…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
A nonlinear adaptive procedure for optimising both the schemes in time and space is proposed in view of increasing the numerical efficiency and reducing the computational time. The method is based on a four-parameter family of schemes we…
Sensitivity analysis plays an important role in searching for constitutive parameters (e.g. permeability) subsurface flow simulations. The mathematics behind is to solve a dynamic constrained optimization problem. Traditional methods like…
An efficient numerical scheme for solving transport equations for tokamak plasmas within an integrated modelling framework is presented. The plasma transport equations are formulated as diffusion-advection equations in two coordinates (a…
Context: The paradigm of convection in solar-like stars is questioned based on recent solar observations. Aims: The primary aim is to study the effects of surface-driven entropy rain on convection zone structure and flows. Methods:…