David Zorío

David Zorío
University of Concepción · Centro de Investigación en Ingeniería Matemática

About

12
Publications
1,648
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
108
Citations
Citations since 2016
11 Research Items
103 Citations
20162017201820192020202120220510152025
20162017201820192020202120220510152025
20162017201820192020202120220510152025
20162017201820192020202120220510152025

Publications

Publications (12)
Article
We present a new family of high-order shock-capturing finite difference numerical methods for systems of conservation laws. These methods, called Adaptive Compact Approximation Taylor (ACAT) schemes, use centered (2p+1)-point stencils, where p may take values in {1,2,…,P} according to a new family of smoothness indicators in the stencils. The metho...
Article
Full-text available
The goal of this work is to introduce new families of shock-capturing high-order numerical methods for systems of conservation laws that combine Fast WENO (FWENO) and Optimal WENO (OWENO) reconstructions with Approximate Taylor methods for the time discretization. FWENO reconstructions are based on smoothness indicators that require a lower number...
Article
An efficient approximate version of implicit Taylor methods for initial-value problems of systems of ordinary differential equations (ODEs) is introduced. The approach, based on an approximate formulation of Taylor methods, produces a method that requires less evaluations of the function that defines the ODE and its derivatives than the usual versi...
Article
A new method for the numerical solution of ODEs is presented. This approach is based on an approximate formulation of the Taylor methods that has a much easier implementation than the original Taylor methods, since only the functions in the ODEs, and not their derivatives, are needed, just as in classical Runge–Kutta schemes. Compared to Runge–Kutt...
Article
A new method for the numerical solution of ODEs is presented. This approach is based on an approximate formulation of the Taylor methods that has a much easier implementation than the original Taylor methods, since only the functions in the ODEs, and not their derivatives, are needed, just as in classical Runge–Kutta schemes. Compared to Runge–Kutt...
Article
The Lax–Wendroff time discretization is an alternative method to the popular total variation diminishing Runge–Kutta time discretization of discontinuous Galerkin schemes for the numerical solution of hyperbolic conservation laws. The resulting fully discrete schemes are known as LWDG and RKDG methods, respectively. Although LWDG methods are in gen...
Article
Full-text available
A high order time stepping applied to spatial discretizations provided by the method of lines for hyperbolic conservations laws is presented. This procedure is related to the one proposed in Qiu and Shu (SIAM J Sci Comput 24(6):2185–2198, 2003) for numerically solving hyperbolic conservation laws. Both methods are based on the conversion of time de...
Article
Full-text available
The design of numerical boundary conditions is a challenging problem that has been tackled in different ways depending on the nature of the problem and the numerical scheme used to solve it. In this paper we present a new weighted extrapolation technique which entails an improvement with respect to the technique that was developed in [1]. This tech...
Article
We prove that a semidiscrete $(2r+1)$-point scheme for quasilinear first order PDE cannot attain an order higher than $2r$. Moreover, if the forward Euler fully discrete scheme obtained from the linearization about any constant state of the semidiscrete scheme is stable, then the upper bound for the order of the scheme is $2r-1$. This bound is atta...
Chapter
The design of numerical boundary conditions in high order schemes is a challenging problem that has been tackled in different ways depending on the nature of the problem and the scheme used to solve it numerically. In this paper we propose a technique to extrapolate the information from the computational domain to ghost cells for schemes with struc...
Article
The application of suitable numerical boundary conditions for hyperbolic conservation laws on domains with complex geometry has become a problem with certain difficulty that has been tackled in different ways according to the nature of the numerical methods and mesh type. In this paper we present a technique for the extrapolation of information fro...

Network

Cited By