Related papers: The "Sphered Cube": A New Method for the Solution …
In this thesis, a new approach for constructing subdivision algorithms for generalized quadratic and cubic B-spline subdivision for subdivision surfaces and volumes is presented. First, a catalog of quality criteria for these subdivision…
A fourth-order dispersive flow equation for closed curves on the canonical two-dimensional unit sphere arises in some contexts in physics and fluid mechanics. In this paper, a geometric generalization of the sphere-valued model is…
The closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding method developed to solve a variety of partial differential equations (PDEs) on smooth surfaces, using a closest point representation…
We present a new implementation of the geometric method of Cullen & Purser (1984) for solving the semi-geostrophic Eady slice equations which model large scale atmospheric flows and frontogenesis. The geometric method is a Lagrangian…
First-order systems of hyperbolic partial differential equations (PDEs) occur ubiquitously throughout computational physics, commonly used in simulations of fluid turbulence, shock waves, electromagnetic interactions, and even general…
Polynomial spectral methods produce fast, accurate, and flexible solvers for broad ranges of PDEs with one bounded dimension, where the incorporation of general boundary conditions is well understood. However, automating extensions to…
This paper deals with the numerical computations of two space dimensional time dependent parabolic partial differential equations by adopting adopting an optimal five stage fourth-order strong stability preserving Runge Kutta (SSP-RK54)…
We develop a volume penalization method for inhomogeneous Neumann boundary conditions, generalizing the flux-based volume penalization method for homogeneous Neumann boundary condition proposed by Kadoch et al. [J. Comput. Phys. 231 (2012)…
While granular segregation in partially filled containers has been studied extensively, granular dynamics in densely filled spheres is not fully understood. Here, surface band segregation and granular convection are reported in a rotating…
Partial differential equations with distributional sources---in particular, involving (derivatives of) delta distributions---have become increasingly ubiquitous in numerous areas of physics and applied mathematics. It is often of…
Existing structural analysis methods may fail to find all hidden constraints for a system of differential-algebraic equations with parameters if the system is structurally unamenable for certain values of the parameters. In this paper, for…
To investigate the attenuation of turbulence in a periodic cube due to the addition of spherical solid particles, we conduct direct numerical simulations using an immersed boundary method with resolving flow around each particle. Numerical…
We present a novel staggered semi-implicit hybrid FV/FE method for the numerical solution of the shallow water equations at all Froude numbers on unstructured meshes. A semi-discretization in time of the conservative Saint-Venant equations…
The main objective of this paper is to develop a general method of geometric discretization for infinite-dimensional systems and apply this method to the EPDiff equation. The method described below extends one developed by Pavlov et al. for…
The goal of the present work is to solve a linear dispersive equation with variable coefficient advection on an unbounded domain. In this setting, transparent boundary conditions are vital to allow waves to leave (or even re-enter) the,…
This work presents a novel framework for spherical mesh parameterization. An efficient angle-preserving spherical parameterization algorithm is introduced, which is based on dynamic Yamabe flow and the conformal welding method with solid…
The extended form of the classical polynomial cubic B-spline function is used to set up a collocation method for some initial boundary value problems derived for the Korteweg-de Vries-Burgers equation. Having nonexistence of third order…
In this work we study the dynamic behaviour of compound shells of revolution partially filled with an ideal incompressible fluid based on boundary-value problems. New analytical mathematical model with corresponding discrete scheme for the…
We develop an immersed boundary (IB) method for modeling flows around fixed or moving rigid bodies that is suitable for a broad range of Reynolds numbers, including steady Stokes flow. The spatio-temporal discretization of the fluid…
We provide a new algorithm for the treatment of the deconvolution problem on the sphere which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. We establish upper bounds for the…