75 documents found, page 1 of 8
Very high-order finite difference method on arbitrary geometries with Cartesian...
Clain, Stéphane; Lopes, Diogo; Pereira, Rui M. S.; Pereira, Paulo A.An arbitrary order finite difference method for solving non-linear convection Diffusion Reaction equations in curved boundary domains with Cartesian grid is proposed. Ghost points' values are determined with the Reconstruction Off-Site Data based on a polynomial interpolation using the least square method with constraints to enforce the boundary conditions. We propose a second-, fourth-, and sixth-order schemes...
Stencil and kernel optimisation for mesh-free very high-order generalised finit...
Clain, Stéphane; Figueiredo, JorgeGeneralised Finite Difference Methods and similar mesh-free methods (Point set method, Multipoint method) are based on three main ingredients: a stencil around the reference node, a polynomial reconstruction and a weighted functional to provide the relation sbetween the derivatives at the reference node and the nodes of the stencil.Very few studies were dedicated to the optimal choice of the stencil together wi...
Very high-order accurate discontinuous Galerkin method for curved boundaries wi...
Santos, Milene; Araújo, Adérito; Barbeiro, Sílvia; Clain, Stéphane; Costa, Ricardo Daniel Pereira da; Machado, Gaspar J.Preserving the optimal convergence order of discontinuous Galerkin (DG) discretisations in curved domains is a critical and well-known issue. The proposed approach relies on the reconstruction for off-site data (ROD) method developed originally within the finite volume framework. The main advantages are simplicity, since the PDE solver only considers polyg- onal domains, and versatility, since any type of bound...
Compact schemes in time with applications to partial differential equations
Clain, Stéphane; Machado, Gaspar J.; Malheiro, M.T.We propose a new class of fourth-and sixth-order schemes in time for parabolic and hyperbolic equations. The method follows the compact scheme methodology by elaborating implicit relations between the approximations of the function and its derivatives. We produce a series of A-stable methods with low dispersion and high accuracy. Several benchmarks for linear and non-linear Ordinary Differential Equations demon...
Imposing slip conditions on curved boundaries for 3D incompressible flows with ...
Costa, Ricardo Daniel Pereira da; Clain, Stéphane; Machado, Gaspar J.; Nóbrega, J. M.; Beirão da Veiga, Hugo; Crispo, FrancescaThe conventional no-slip boundary condition does not always hold in several fluid flow applications and must be replaced with appropriate slip conditions according to the wall and fluid properties. However, not only slip boundary conditions are still a subject of discussion among fluid dynamicists, but also their numerical treatment is far from being well-developed, particularly in the context of very high-orde...
Structural schemes for one dimension stationary equations
Clain, Stéphane; Pereira, Rui M. S.; Pereira, Paulo A.; Lopes, DiogoIn this paper, we propose a new paradigm for finite differences numerical methods, based on compact schemes to provide high order accurate approximations of a smooth solution. The method involves its derivatives approximations at the grid points and the construction of structural equations deriving from the kernels of a matrix that gathers the variables belonging to a small stencil. Numerical schemes involve co...
Compact schemes in time with applications to partial differential equations
Clain, Stéphane; Machado, Gaspar J.; Malheiro, M. TeresaWe propose a new class of fourth-and sixth-order schemes in time for parabolic and hyperbolic equations. The method follows the compact scheme methodology by elaborating implicit relations between the approximations of the function and its derivatives. We produce a series of A-stable methods with low dispersion and high accuracy. Several benchmarks for linear and non-linear Ordinary Differential Equations demon...
Smoothed particle hydrodynamics modeling of elevated structures impacted by tsu...
Reis, Cláudia; Barbosa, André R.; Figueiredo, Jorge; Clain, Stéphane; Lopes, Mário; Baptista, Maria AnaAccurate characterization of the response of coastal structures when subjected to tsunami-like waves is important for structural engineering assessment and design. The weakly-compressive Smoothed Particle Hydrodynamic (SPH) model can theoretically investigate such phenomena in both horizontal and vertical directions. Yet, the convergence of the solutions is sensitive to physical and numerical parameters used in...
A new stabilised scheme for the Richards’ equation with evapotranspiration
Machado, Gaspar J.; Pereira, Rui M. S.; Clain, Stéphane; Araújo, Nuno Miguel Faria; Lopes, S. O.A new second-order stabilised numerical method for the Richards' equation with source term is proposed to solve the water infiltration in porous soil. This new method to solve Richard's equation is based on a modification of the head pressure representation with respect to the water content together with the hydraulic conductivity. We show that the modified relations provide stability while preserving the order...
Experimentally validated numerical models to assess tsunami hydrodynamic force ...
Reis, Cláudia; Clain, Stéphane; Figueiredo, Jorge; Barbosa, André R.; Baptista, Maria Ana; Lopes, MárioRecently, the North American and Japanese authorities began combining the tsunami forces with other loads in their structural design guidelines. Nonetheless, due to the infrequent nature of tsunamis, the provisions may benefit from complementary insights on the qualitative and quantitative characterization of the extreme phenomena and their interaction with coastal structures. The goal of this paper is to explo...