Numerical modeling of neutron flux in hexagonal geometry
Numerical modeling of neutron transport - finite volume method, residual distribution schemes
Numerical modeling of the simultaneous heat and moisture transfer
Numerical modelling and simulation of liquid-impelled loop reactor.
Numerical modelling of a bridge subjected to simultaneous effect of a moving load and a vertical seismic ground excitation
A simple beam subjected to a row of regularly distributed moving forces and simultaneous vertical motions of its supports is described using a simplified theoretical model and a finite differences approach. Several levels of simplification of the structure and input data are supposed. Numerical results confirm legitimacy of the assumptions.
Numerical Modelling of Contact Elastic-Plastic Flows
Wilkins' method has been successfully used since early 60s for numerical simulation of high velocity contact elastic-plastic flows. The present work proposes some effective modifications of this method including more sophisticated material model including the Baushinger effect; modification of the algorithm based on correction of the initial configuration of a solid; a contact algorithm based on the idea of a mild contact.
Numerical modelling of flow in lower urinary tract using high-resolution methods
We propose a new numerical scheme based on the finite volumes to simulate the urethra flow based on hyperbolic balance law. Our approach is based on the Riemann solver designed for the augmented quasilinear homogeneous formulation. The scheme has general semidiscrete wave–propagation form and can be extended to arbitrary high order accuracy. The first goal is to construct the scheme, which is well balanced, i.e. maintains not only some special steady states but all steady states which can occur....
Numerical modelling of river flow (numerical schemes for one type of nonconservative systems
In this paper we propose a new numerical scheme to simulate the river flow in the presence of a variable bottom surface. We use the finite volume method, our approach is based on the technique described by D. L. George for shallow water equations. The main goal is to construct the scheme, which is well balanced, i.e. maintains not only some special steady states but all steady states which can occur. Furthermore this should preserve nonnegativity of some quantities, which are essentially nonnegative...
Numerical modelling of semi-coercive beam problem with unilateral elastic subsoil of Winkler's type
A non-linear semi-coercive beam problem is solved in this article. Suitable numerical methods are presented and their uniform convergence properties with respect to the finite element discretization parameter are proved here. The methods are based on the minimization of the total energy functional, where the descent directions of the functional are searched by solving the linear problems with a beam on bilateral elastic ``springs''. The influence of external loads on the convergence properties is...
Numerical modelling of steady and unsteady flows of generalized Newtonian fluids
This work presents the numerical solution of laminar incompressible viscous flow in a three dimensional branching channel with circular cross section for generalized Newtonian fluids. This model can be generalized by cross model in shear thinning meaning. The governing system of equations is based on the system of balance laws for mass and momentum. Numerical tests are performed on a three dimensional geometry, the branching channel with one entrance and two outlet parts. Numerical solution of the...
Numerical modelling of tube fixing in the heat exchanger of a nuclear power plant
Numerical modelling of viscous and viscoelastic fluids flow through the branching channel
The aim of this paper is to describe the numerical results of numerical modelling of steady flows of laminar incompressible viscous and viscoelastic fluids. The mathematical models are Newtonian and Oldroyd-B models. Both models can be generalized by cross model in shear thinning meaning. Numerical tests are performed on three dimensional geometry, a branched channel with one entrance and two output parts. Numerical solution of the described models is based on cell-centered finite volume method...
Numerical modelling of viscous incompressible flow [Abstract of thesis]
Numerical operations among rational matrices: standard techniques and interpolation
Numerical operations on and among rational matrices are traditionally handled by direct manipulation with their scalar entries. A new numerically attractive alternative is proposed here that is based on rational matrix interpolation. The procedure begins with evaluation of rational matrices in several complex points. Then all the required operations are performed consecutively on constant matrices corresponding to each particular point. Finally, the resulting rational matrix is recovered from the...
Numerical optimization of parameters in systems of differential equations
We present results on the estimation of unknown parameters in systems of ordinary differential equations in order to fit the output of models to real data. The numerical method is based on the nonlinear least squares problem along with the solution of sensitivity equations corresponding to the differential equations. We will present the performance of the method on the problem of fitting the output of basic compartmental epidemic models to data from the Covid-19 epidemic. This allows us to draw...
Numerical precision for differential inclusions with uniqueness
In this article, we show the convergence of a class of numerical schemes for certain maximal monotone evolution systems; a by-product of this results is the existence of solutions in cases which had not been previously treated. The order of these schemes is in general and when the only non Lipschitz continuous term is the subdifferential of the indicatrix of a closed convex set. In the case of Prandtl’s rheological model, our estimates in maximum norm do not depend on spatial dimension.
Numerical precision for differential inclusions with uniqueness
In this article, we show the convergence of a class of numerical schemes for certain maximal monotone evolution systems; a by-product of this results is the existence of solutions in cases which had not been previously treated. The order of these schemes is 1/2 in general and 1 when the only non Lipschitz continuous term is the subdifferential of the indicatrix of a closed convex set. In the case of Prandtl's rheological model, our estimates in maximum norm do not depend on spatial dimension. ...
Numerical Procedure for Solving a Minimization Eigenvalue Problem.
Numerical procedure to approximate a singular optimal control problem
In this work we deal with the numerical solution of a Hamilton-Jacobi-Bellman (HJB) equation with infinitely many solutions. To compute the maximal solution – the optimal cost of the original optimal control problem – we present a complete discrete method based on the use of some finite elements and penalization techniques.
Numerical realization of the Bayesian inversion accelerated using surrogate models
The Bayesian inversion is a natural approach to the solution of inverse problems based on uncertain observed data. The result of such an inverse problem is the posterior distribution of unknown parameters. This paper deals with the numerical realization of the Bayesian inversion focusing on problems governed by computationally expensive forward models such as numerical solutions of partial differential equations. Samples from the posterior distribution are generated using the Markov chain Monte...