Simulation Of Nonlinear Problems Research Articles

Supercomputer simulation of nonlinear problems of fluid dynamics in cores

This report focuses on technology of supercomputer simulation of nonlinear processes in the cores, extracted from oil and gas production wells in order to study the properties of hydrocarbon reservoirs. One of modern approaches to solving these kind problems is to create multiphysical mathematical model of core for its study by computer methods. This approach minimizes the number of natural experiments and predicts the evolution of layers properties. Also it allows to predict oil and gas recovery of layers for a long time period. However, implementation of this technology called “virtual core” requires the following: 1) to create multiparametrical model of core as close as possible to the reality; 2) to include the multicomponent and multiphase composition and complex real geometry of core in consideration; 3) to develop a computational framework for modeling the seepage of multicomponent liquid and gas mixtures through the core; 4) to carry out large-scale calibration calculations. In this paper, an attempt to create such a multifactor mathematical model and computational foundations for its computing and supercomputing analysis is made.

Implementation of a damage model in a finite element program for computation of structures under dynamic loading

This work is a numerical simulation of nonlinear problems of the damage process and fracture of quasi-brittle materials especially concrete. In this study, we model the macroscopic behavior of concrete material, taking into account the phenomenon of damage. J. Mazars model whose principle is based on damage mechanics has been implemented in a finite element program written Fortran 90, it takes into account the dissymmetry of concrete behavior in tension and in compression, this model takes into account the cracking tensile and rupture in compression. It is a model that is commonly used for static and pseudo-static systems, but in this work, it was used in the dynamic case.

The multi-water-bag equations for collisionless kinetic modeling

In this paper we consider the multi-water-bag model for collisionless kinetic equations. The multi-water-bag representation of the statistical distribution function of particles can be viewed as a special class of exact weak solution of the Vlasov equation, allowing to reduce this latter into a set of hydrodynamic equations while keeping its kinetic character. After recalling the link of the multi-water-bag model with kinetic formulation of conservation laws, we derive different multi-water-bag (MWB) models, namely the Poisson-MWB, the quasineutral-MWB and the electromagnetic-MWB models. These models are very promising because they reveal to be very useful for the theory and numerical simulations of laser-plasma and gyrokinetic physics. In this paper we prove some existence and uniqueness results for classical solutions of these different models. We next propose numerical schemes based on Discontinuous Garlerkin methods to solve these equations. We then present some numerical simulations of non linear problems arising in plasma physics for which we know some analytical results.

Electric simulation of nonlinear problems in heat and mass transfer

A method is described for the electric simulation of nonlinear heat- and mass-transfer problems on two resistance networks. The temperature is simulated on one network and the masstransfer potential on the other. The mass-transfer potential has a discontinuity of the first kind because of a moving zone boundary on which intense phase transitions occur.