High order accurate two-step approximations for hyperbolic equations
High resolution schemes for hyperbolic conservation laws
Hybrid central-upwind schemes for numerical resolution of two-phase flows
In this paper we present a methodology for constructing accurate and efficient hybrid central-upwind (HCU) type schemes for the numerical resolution of a two-fluid model commonly used by the nuclear and petroleum industry. Particularly, we propose a method which does not make use of any information about the eigenstructure of the jacobian matrix of the model. The two-fluid model possesses a highly nonlinear pressure law. From the mass conservation equations we develop an evolution equation which...
Hybrid central-upwind schemes for numerical resolution of two-phase flows
In this paper we present a methodology for constructing accurate and efficient hybrid central-upwind (HCU) type schemes for the numerical resolution of a two-fluid model commonly used by the nuclear and petroleum industry. Particularly, we propose a method which does not make use of any information about the eigenstructure of the Jacobian matrix of the model. The two-fluid model possesses a highly nonlinear pressure law. From the mass conservation equations we develop an evolution equation which...
Identification of nonlinear coefficient in a transport equation.
Immersed boundary methods for the numerical simulation of incompressible aerodynamics and fluid-structure interactions
In this work three branches of Immersed Boundary Methods (IBM) are described and validated for incompressible aerodynamics and fluid-structure interactions. These three approaches are: Cut Cell method, Vortex-Penalization method and Forcing method. The first two techniques are validated for external bluff-body flow around a circular obstacle. The last one is used to predict the deformations of an elastic membrane immersed in a fluid. The paper confirms the ability of this family of numerical schemes...
Immersed interface method for a system of linear reaction-diffusion equations with nonlinear singular own sources
Implicit difference method for nonlinear first order partial differential equations.
Implicit difference methods for nonlinear first order partial functional differential systems
Initial problems for nonlinear hyperbolic functional differential systems are considered. Classical solutions are approximated by solutions of suitable quasilinear systems of difference functional equations. The numerical methods used are difference schemes which are implicit with respect to the time variable. Theorems on convergence of difference schemes and error estimates of approximate solutions are presented. The proof of the stability is based on a comparison technique with nonlinear estimates...
Implicit difference methods for quasilinear parabolic functional differential systems.
Implicit difference methods for quasilinear parabolic functional differential problems of the Dirichlet type
Classical solutions of quasilinear functional differential equations are approximated with solutions of implicit difference schemes. Proofs of convergence of the difference methods are based on a comparison technique. Nonlinear estimates of the Perron type with respect to the functional variable for given functions are used. Numerical examples are given.
Implicit difference scheme for the numerical resolution of the Charney-Obukhov equation with variable coefficients.
Implicit difference schemes for mixed problems related to parabolic functional differential equations
Solutions of initial boundary value problems for parabolic functional differential equations are approximated by solutions of implicit difference schemes. The existence and uniqueness of approximate solutions is proved. The proof of the stability is based on a comparison technique with nonlinear estimates of the Perron type for given operators. It is shown that the new methods are considerably better than the explicit difference schemes. Numerical examples are presented.
Iterative schemes for high order compact discretizations to the exterior Helmholtz equation∗
We consider high order finite difference approximations to the Helmholtz equation in an exterior domain. We include a simplified absorbing boundary condition to approximate the Sommerfeld radiation condition. This yields a large, but sparse, complex system, which is not self-adjoint and not positive definite. We discretize the equation with a compact fourth or sixth order accurate scheme. We solve this large system of linear equations with a Krylov subspace iterative method. Since the method converges...
Iterative schemes for high order compact discretizations to the exterior Helmholtz equation∗
We consider high order finite difference approximations to the Helmholtz equation in an exterior domain. We include a simplified absorbing boundary condition to approximate the Sommerfeld radiation condition. This yields a large, but sparse, complex system, which is not self-adjoint and not positive definite. We discretize the equation with a compact fourth or sixth order accurate scheme. We solve this large system of linear equations with a Krylov subspace iterative method. Since the method converges...
Jeux différentiels et approximation numérique de fonctions valeur. 2e partie : étude numérique
Konvergenz eines Differenzverfahrens für quasilineare parabolische Anfangs-Randwertprobleme in Zylindersymmetrie.
-error estimates of the extrapolated Crank-Nicolson discontinuous Galerkin approximations for nonlinear Sobolev equations.
Lagrangian approach to deriving energy-preserving numerical schemes for the Euler–Lagrange partial differential equations
We propose a Lagrangian approach to deriving energy-preserving finite difference schemes for the Euler–Lagrange partial differential equations. Noether’s theorem states that the symmetry of time translation of Lagrangians yields the energy conservation law. We introduce a unique viewpoint on this theorem: “the symmetry of time translation of Lagrangians derives the Euler–Lagrange equation and the energy conservation law, simultaneously.” The proposed method is a combination of a discrete counter...
Local one-dimensional scheme for the third boundary value problem for the heat equation.