Raimondas Čiegis

On Parallel Numerical Algorithms for Simulating Industrial Filtration Problems

Abstract The performance of oil filters used in the automotive industry can be significantly improved, especially when computer simulation is an essential component of the design process. In this paper, we consider parallel numerical algorithms for solving mathematical models describing the process of filtration, filtering solid particles out of liquid oil. The Navier — Stokes — Brinkmann system of equations is used to describe the laminar flow of incompressible isothermal oil. The space discretization in the complicated filter geometry is based on the finite-volume method. Special care is taken for an accurate approximation of the velocity and pressure on the interface between the fluid and the porous media. The time discretization used here is a proper modification of the fractional time step discretization (cf. Chorin scheme) of the Navier- Stokes equations, where the Brinkmann term is considered in both the prediction and the correction substeps. A data decomposition method is used to develop a parallel algorithm, where the domain is distributed among the processors by using a structured reference grid. The MPI library is used to implement the data communication part of the algorithm. A theoretical model is proposed for the estimation of the complexity of the given parallel algorithm and a scalability analysis is done on the basis of this model. The results of the computational experiments are presented, and the accuracy and efficiency of the parallel algorithm is tested on real industrial geometries.

NUMERICAL SOLUTION OF PARABOLIC PROBLEMS WITH NONLOCAL BOUNDARY CONDITIONS

In this article, the one-dimensional parabolic equation with three types of integral nonlocal boundary conditions is approximated by the implicit Euler finite difference scheme. Stability analysis is done in the maximum norm and it is proved that the radius of the stability region and the stiffness of the discrete scheme depends on the signs of coefficients in the nonlocal boundary condition. The known stability results are improved. In the case of a plain integral boundary condition, the conditional convergence rate is proved and the regularization relation between discrete time and space steps is proposed. The accuracy of the obtained estimates is illustrated by results of numerical experiments.

A Parallel Solver for the 3D Simulation of Flows Through Oil Filters

The performance of oil filters used in automotive engines and other areas can be significantly improved using computer simulation as an essential component of the design process. In this chapter, a parallel solver for the 3D simulation of flows through oil filters is presented. The Navier–Stokes–Brinkmann system of equations is used to describe the coupled laminar flow of incompressible isothermal oil through open cavities and cavities with filtering porous media. The space discretization in the complicated filter geometry is based on the finite-volume method.

Parallel global optimization of foundation schemes in civil engineering

The important problem in civil engineering is obtaining optimal pile placement schemes for grillage-type foundations. The standard technique for solution of problem is application of local optimization methods, starting from initial guess obtained by means of engineering heuristics. We propose a new technology based on the use of global optimization algorithms, which are implemented as the “black-boxes”. In the real world applications the problems of interest involve till 500 design parameters. Therefore such problems can not be solved using one processor due to the huge CPU and computer memory requirements. We propose a parallel version of global optimization algorithm. The results of computational experiments for a number of practical problems are presented. Efficiency of suggested parallel algorithms is investigated and results for different clusters of workstations are presented.

One Application of the Parallelization Tool of Master–Slave Algorithms

The paper analyzes the performance of parallel global optimization algorithm, which is used to optimize grillage-type foundations. The parallel algorithm is obtained by using the automatic parallelization tool. We describe briefly the layer structure of the Master–Slave Template library and present a detailed mathematical formulation of the application problem. Experiments are done on the homogeneous computer cluster of 7 IBM machines RS6000. The results of experiments are presented.

A Parallel Solver for the Design of Oil Filters

Nowadays, it is widely recognized that computer simulation plays a crucial role in designing oil filters used in the automotive industry. However, even a single direct simulation of the flow usually requires significant computational resources. Thus, it is obvious that solution of optimization problems is only feasible using parallel computers and algorithms.In this paper, we present a general master-slave parallel template, which was specially designed for the easy integration of direct parallel solvers into a parallel optimization tool. We show how an already existing direct solver for the 3D simulation of flow through the oil filter is integrated into our template to obtain a parallel optimization solver. Some capabilities and performance of this solver are demonstrated by solving geometry optimization problem of a filter element.

Effective numerical integration of traveling wave model for edge‐emitting broad‐area semiconductor lasers and amplifiers

Abstract We consider a system of 1 + 2 dimensional partial differential equations which describes dynamics of edge‐emitting broad area semiconductor lasers and amplifiers. The given problem is defined on the unbounded domain. After truncating this domain and defining an auxiliary 1 + 1 dimensional linear Schrodinger problem supplemented with different artificial boundary conditions, we propose an effective strategy allowing to get a solution of the full problem with a satisfactory precision in a reasonable time. For further speed up of the numerical integration, we develop a parallel version of the algorithm.

Numerical Algorithms for Schrödinger Equation with Artificial Boundary Conditions

We consider a one-dimensional linear Schrödinger problem defined on an infinite domain and approximated by the Crank–Nicolson type finite difference scheme. To solve this problem numerically we restrict the computational domain by introducing the reflective, absorbing or transparent artificial boundary conditions. We investigate the conservativity of the discrete scheme with respect to the mass and energy of the solution. Results of computational experiments are presented and the efficiency of different artificial boundary conditions is discussed.

Effective Numerical Algorithm for Simulations of Beam Stabilization in Broad Area Semiconductor Lasers and Amplifiers

AbstractA 2 + 1 dimensional PDE traveling wave model describing spatial-lateral dynamics of edge-emitting broad area semiconductor devices is considered. A numerical scheme based on a split-step Fourier method is presented. The domain decomposition method is used to parallelize the sequential algorithm. The parallel algorithm is implemented by using Message Passing Interface system, results of computational experiments are presented and the scalability of the algorithm is analyzed. Simulations of the model equations are used for optimizing of existing devices with respect to the emitted beam quality, as well as for creating and testing of novel device design concepts.

Analysis of upwind and high‐resolution schemes for solving convection dominated problems in porous media

Abstract The conservation laws governing the multiphase flows in porous media are often convection‐dominated and have a steep fronts that require accurate resolution. Standard discretization methods of the convection terms do not perform well for such problems. The main aim of this work is to analyze the use of upwind and high‐ resolution schemes in such cases. First, we use a first differential approximation method to perform a theoretical analysis of a standard upwind approximation and different time stepping schemes for the linear hyperbolic equations in 1‐ and 2D. Next, we present a popular approach to reduce the amount of numerical diffusion introduced by upwind approximation ‐ high‐resolution schemes. We compare our implementation of one of the recently proposed central‐upwind schemes against the upwind schemes on several test problems based on Buckley‐Leverett equation and discuss the results. Finally, a parallel version of central‐upwind scheme in 2D is presented. It was implemented using our C++ ...