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The Immersed Boundary method has evolved into one of the most useful computational methods in studying fluid structure interaction. On the other hand, the Immersed Boundary method is also known to suffer from a severe timestep stability…
We present a Newton-Krylov solver for a viscous-plastic sea-ice model. This constitutive relation is commonly used in climate models to describe the material properties of sea ice. Due to the strong nonlinearity introduced by the material…
Singularly perturbed systems (SPSs) are prevalent in engineering applications, where numerically solving their initial value problems (IVPs) is challenging due to stiffness arising from multiple time scales. Classical explicit methods…
An in-house large eddy simulation tool is developed in order to reproduce high fidelity results of compressible jet flows. The large eddy simulation formulation is written using the finite difference approach, with an explicit time…
Numerical models are widely used to simulate the earth system, but they are computationally expensive and often depend on many uncertain input parameters. Their effective use requires calibration and uncertainty quantification, which…
The isentropic compressible Cahn-Hilliard-Navier-Stokes equations is a system of fourth-order partial differential equations that model the evolution of some binary fluids under convection. The purpose of this paper is the design of…
Icy satellites host topography at many length scales, from rifts and craters on the small end to equatorial-pole shell thickness differences that are comparable to these bodies' circumference. The rate of topographic evolution depends on…
The reduction of computational costs for marine ecosystem models is important for the investigation and detection of the relevant biogeochemical processes because such models are computationally expensive. In order to lower these…
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…
In the numerical solution of partial differential equations using a method-of-lines approach, the availability of high order spatial discretization schemes motivates the development of sophisticated high order time integration methods. For…
Coarse-grained modeling and efficient computer simulations are critical to the study of complex molecular processes with many degrees of freedom and multiple spatiotemporal scales. Variational implicit-solvent model (VISM) for biomolecular…
In this paper a numerical procedure to simulate low diffusivity scalar turbulence is presented. The method consists of using a grid for the advected scalar with a higher spatial resolutions than that of the momentum. The latter usually…
Innovative numerical scheme studied in this work enables to overcome two main limitations of Building Performance Simulation (BPS) programs as high computational cost and the choice of a very fine numerical grid. The method, called…
Energy loss through optically thin radiative cooling plays an important part in the evolution of astrophysical gas dynamics and should therefore be considered a necessary element in any numerical simulation. Although the addition of this…
The phase field method is an effective tool for modeling microstructure evolution in materials. Many efficient implicit numerical solvers have been proposed for phase field simulations under uniform and time-invariant model parameters. We…
The weathering crust is a layer of porous ice that can form at the surface of an ice sheet. It grows and decays in response changing weather and climate conditions, affecting the albedo, the melt rate, and the transport of meltwater across…
This study investigates numerical methods to solve nonlinear transport problems characterized by various sorption isotherms with a focus on the Freundlich type of isotherms. We describe and compare second order accurate numerical schemes,…
In this paper, we develop a class of robust numerical methods for solving dynamical systems with multiple time scales. We first represent the solution of a multiscale dynamical system as a transformation of a slowly varying solution. Then,…
The expedient design of precision components in aerospace and other high-tech industries requires simulations of physical phenomena often described by partial differential equations (PDEs) without exact solutions. Modern design problems…
Simulation of unsteady creeping flows in complex geometries has traditionally required the use of a time-stepping procedure, which is typically costly and unscalable. To reduce the cost and allow for computations at much larger scales, we…