36 citations · 179 across the 12 of their papers we have counts for
12 papers
High-order fully well-balanced numerical methods for one-dimensional blood flow with discontinuous properties, friction and gravity
Ernesto Pimentel-García, Lucas O. Müller, Carlos Parés
We present well-balanced, high-order, semi-discrete numerical schemes for one-dimensional blood flow models with discontinuous mechanical properties and algebraic source terms repr…
Collocation Methods for High-Order Well-Balanced Methods for Systems of Balance Laws
Irene Gómez-Bueno, Manuel Jesús Castro Díaz, Carlos Parés +1
In some previous works, two of the authors introduced a technique to design high-order numerical methods for one-dimensional balance laws that preserve all their stationary solutio…
High-order well-balanced methods for systems of balance laws: a control-based approach
Irene Gómez-Bueno, Manuel Jesús Castro Díaz, Carlos Parés
In some previous works, two of the authors have introduced a strategy to develop high-order numerical methods for systems of balance laws that preserve all the stationary solutions…
Approximate well-balanced WENO finite difference schemes using a global-flux quadrature method with multi-step ODE integrator weights
Maria Kazolea, Carlos Parés Madroñal, Mario Ricchiuto
In this work, high-order discrete well-balanced methods for one-dimensional hyperbolic systems of balance laws are proposed. We aim to construct a method whose discrete steady stat…
High-order WENO finite-difference methods for hyperbolic nonconservative systems of Partial Differential Equations
B. Ren, C. Parés
This work aims to extend the well-known high-order WENO finite-difference methods for systems of conservation laws to nonconservative hyperbolic systems. The main difficulty of the…
An almost fail-safe a-posteriori limited high-order CAT scheme
E. Macca, R. Loubere, C. Pares +1
In this paper we blend the high order Compact Approximate Taylor (CAT) numerical schemes with an a-posteriori Multi-dimensional Optimal Order Detection (MOOD) paradigm to solve hyp…
Well-balanced adaptive compact approximate Taylor methods for systems of balance laws
H. Carrillo, E. Macca, C. Pares +1
Compact Approximate Taylor (CAT) methods for systems of conservation laws were introduced by Carrillo and Pares in 2019. These methods, based on a strategy that allows one to exten…
In-cell Discontinuous Reconstruction path-conservative methods for non conservative hyperbolic systems -- Second-order extension
Ernesto Pimentel-García, Manuel J. Castro, Christophe Chalons +2
We are interested in the numerical approximation of discontinuous solutions in non conservative hyperbolic systems. An extension to second-order of a new strategy based on in-cell…
An order-adaptive compact approximation Taylor method for systems of conservation laws
H. Carrillo, E. Macca, G. Russo +2
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 Tay…
Lax Wendroff approximate Taylor methods with fast and optimized weighted essentially non-oscillatory reconstructions
Hugo Carrillo, Carlos Parés, David Zorío
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…
Well-balanced high-order finite difference methods for systems of balance laws
Carlos Parés, Carlos Parés-Pulido
In this paper, high order well-balanced finite difference weighted essentially non-oscillatory methods to solve general systems of balance laws are presented. Two different familie…
Reliability of first order numerical schemes for solving shallow water system over abrupt topography
T. Morales de Luna, M. J. Castro Díaz, C. Parés Madroñal
We compare some first order well-balanced numerical schemes for shallow water system with special interest in applications where there are abrupt variations of the topography. We s…