Search results for "Mesh"

Spectral WENO schemes with Adaptive Mesh Refinement for models of polydisperse sedimentation

2012

The sedimentation of a polydisperse suspension with particles belonging to N size classes (species) can be described by a system of N nonlinear, strongly coupled scalar first-order conservation laws. Its solutions usually exhibit kinematic shocks separating areas of different composition. Based on the so-called secular equation [J. Anderson, Lin. Alg. Appl. 246, 49–70 (1996)], which provides access to the spectral decomposition of the Jacobian of the flux vector for this class of models, Burger et al. [J. Comput. Phys. 230, 2322–2344 (2011)] proposed a spectral weighted essentially non-oscillatory (WENO) scheme for the numerical solution of the model. It is demonstrated that the efficiency …

Adaptive mesh reconstruction for hyperbolic conservation laws with total variation bound

2012

We consider 3-point numerical schemes, that resolve scalar conservation laws, that are oscillatory either to their dispersive or anti-diffusive nature. The spatial discretization is performed over non-uniform adaptively redefined meshes. We provide a model for studying the evolution of the extremes of the oscillations. We prove that proper mesh reconstruction is able to control the oscillations; we provide bounds for the Total Variation (TV) of the numerical solution. We, moreover, prove under more strict assumptions that the increase of the TV, due to the oscillatory behavior of the numerical schemes, decreases with time; hence proving that the overall scheme is TV Increase-Decreasing (TVI…

Fine-Mesh Numerical Simulations for 2D Riemann Problems with a Multilevel Scheme

2001

The numerical simulation of physical problems modeled by systems of conservation laws can be difficult due to the occurrence of discontinuities and other non-smooth features in the solution.

High Order Extrapolation Techniques for WENO Finite-Difference Schemes Applied to NACA Airfoil Profiles

2017

Finite-difference WENO schemes are capable of approximating accurately and efficiently weak solutions of hyperbolic conservation laws. In this context high order numerical boundary conditions have been proven to increase significantly the resolution of the numerical solutions. In this paper a finite-difference WENO scheme is combined with a high order boundary extrapolation technique at ghost cells to solve problems involving NACA airfoil profiles. The results obtained are comparable with those obtained through other techniques involving unstructured meshes.

Computation of travelling wave solutions of scalar conservation laws with a stiff source term

2003

Abstract In this paper we propose a nonoscillatory numerical technique to compute the travelling wave solution of scalar conservation laws with a stiff source term. This procedure is based on the dynamical behavior described by the associated stationary ODE and it reduces/avoids numerical errors usually encountered with these problems, i.e., spurious oscillations and incorrect wave propagation speed. We combine this treatment with either the first order Lax–Friedrichs scheme or the second order Nessyahu–Tadmor scheme. We have tested several model problems by LeVeque and Yee for which the stiffness coefficient can be increased. We have also tested a problem with a nonlinear flux and a discon…

Adaptive mesh refinement techniques for high-order shock capturing schemes for multi-dimensional hydrodynamic simulations

2006

The numerical simulation of physical phenomena represented by non-linear hyperbolic systems of conservation laws presents specific difficulties mainly due to the presence of discontinuities in the solution. State of the art methods for the solution of such equations involve high resolution shock capturing schemes, which are able to produce sharp profiles at the discontinuities and high accuracy in smooth regions, together with some kind of grid adaption, which reduces the computational cost by using finer grids near the discontinuities and coarser grids in smooth regions. The combination of both techniques presents intrinsic numerical and programming difficulties. In this work we present a …

How to apply the Kirkwood–Buff theory to individual species in salt solutions

2013

It is generally assumed that the Kirkwood–Buff (KB) theory cannot be applied to anions and cations individually in a solution, as one cannot simulate this system in an open ensemble due to the electroneutrality constraint. By applying our recently derived KB theory for closed systems, we show that one does have access to single-ion properties in Molecular Dynamics. Our findings are supported by simulations for a model of a salt solution in which particles interact with WCA potentials, as well as for the NaCl/water system using the Particle Mesh Ewald technique for electrostatics.

A more efficient method for clustering sheet metal shapes

2007

The nesting of two-dimensional irregular shapes is a common problem which is frequently encountered by a number of industries where raw material has to be, as economically as possible, cut from a given stock sheet. A frequently recurring problem as far as cutting stock is concerned, is how to obtain the best nesting of some pieces of flat patterns which occupy minimalarea convex enclosure. The area of convex enclosure is related to the convex hull of the union of patterns which can be imagined as a large rubber band surrounding the set of all polygons. Our goal is to automatically obtain the smallest area convex shape containing all the patterns. As a matter of fact, Cheng and Rao have prop…

Mutation Analysis of Core Binding Factor A1 in Patients with Cleidocranial Dysplasia

1999

SummaryCleidocranial dysplasia (CCD) is a dominantly inherited disorder characterized by patent fontanelles, wide cranial sutures, hypoplasia of clavicles, short stature, supernumerary teeth, and other skeletal anomalies. We recently demonstrated that mutations in the transcription factor CBFA1, on chromosome 6p21, are associated with CCD. We have now analyzed the CBFA1 gene in 42 unrelated patients with CCD. In 18 patients, mutations were detected in the coding region of the CBFA1 gene, including 8 frameshift, 2 nonsense, and 9 missense mutations, as well as 2 novel polymorphisms. A cluster of missense mutations at arginine 225 (R225) identifies this residue as crucial for CBFA1 function. …

2017

We propose a mesh-free and discrete (particle-based) multi-physics approach for modelling the hydrodynamics in flexible biological valves. In the first part of this study, the method is successfully validated against both traditional modelling techniques and experimental data. In the second part, it is further developed to account for the formation of solid aggregates in the flow and at the membrane surface. Simulations of various types of aggregates highlight the main benefits of discrete multi-physics and indicate the potential of this approach for coupling the hydrodynamics with phenomena such as clotting and calcification in biological valves.