Vadimas Starikovičius

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.

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.

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++ ...

Parallel solvers for fractional power diffusion problems

Mathematical models with fractional‐order differential operators are computationally expensive due to the non‐local nature of these operators. In this work, we construct and investigate parallel solvers for problems described by fractional powers of elliptic operators, like fractional diffusion. Three state‐of‐the‐art approaches are used to transform the non‐local fractional‐order differential problem into local partial differential equation problems formulated in a space of higher dimension. Numerical schemes and parallel algorithms are developed for all three approaches. The resulting parallel algorithms have very different properties. We investigate the weak and strong scalability of the developed parallel algorithms and compare their parallel performance.

On a numerical subgrid upscaling algorithm for Stokes-Brinkman equations

This paper discusses a numerical subgrid resolution approach for solving the Stokes-Brinkman system of equations, which is describing coupled flow in plain and in highly porous media. Various scientific and industrial problems are described by this system, and often the geometry and/or the permeability vary on several scales. A particular target is the process of oil filtration. In many complicated filters, the filter medium or the filter element geometry are too fine to be resolved by a feasible computational grid. The subgrid approach presented in this paper is aimed at describing how these fine details are accounted for by solving auxiliary problems in appropriately chosen grid cells on a relatively coarse computational grid. This is done via a systematic and careful procedure of modifying and updating the coefficients of the Stokes-Brinkman system in chosen cells. This numerical subgrid approach is motivated from one side from homogenization theory, from which we borrow the formulations for the so-called cell problem, and from the other side from the numerical upscaling approaches, such as Multiscale Finite Volume, Multiscale Finite Element, etc. Results on the algorithms efficiency, both in terms of computational time and memory usage, are presented. Comparison of the full fine grid solution (when possible) of the Stokes-Brinkman system with the subgrid solution of the upscaled Stokes-Brinkman system (including effective permeabilities for the quasi-porous cells), are presented in order to evaluate the accuracy and the efficiency. Advantages and limitations of the considered subgrid approach are discussed.

Development of cloud services for patient-specific simulations of blood flows through aortic valves

The paper presents the development of cloud software services for patient-specific computational analysis of blood flows through the aortic valve on a private university cloud. The main focus is on the software service level at the top of the provided computational platform. Blood flow through the aortic valve was considered as a pilot application of the OpenStack cloud infrastructure. A modelling software environment based on ANSYS Fluent was developed as a software service (SaaS) for the numerical analysis of low flow, low pressure gradient aortic stenosis. Segmentation software services were designed to deal with the patient-specific issues of the computational analysis. User-friendly management tools were developed using Apache jclouds API to enhance the management of OpenStack cloud infrastructure and to increase the accessibility of the required software. The performance of the cloud infrastructure was assessed by testing CPU, memory bandwidth, disk I/O and the developed software service for medical computations. The performance measured on Xen hardware virtual machines, KVM virtual machines and Docker containers were compared with the performance obtained by using the native hardware.

The Finite Difference Scheme for 3d Mathematical Modeling of a Wood Drying Process

Abstract This work discusses issues on the design and analysis of finite difference schemes for 3D modeling the process of moisture motion in the wood. A new finite difference scheme is proposed. The stability and convergence in the maximum norm are proved for Robin boundary conditions. The influence of boundary conditions is investigated, and results of numerical experiments are presented.

On iterative solvers for non‐Newtonian flow equations

Purpose – This study proposes to develop and investigate different iterative solvers for non‐Newtonian flow equations.Design/methodology/approach – Existing approaches for the time discretization of the flow equation and for an iterative solution of the discrete systems are discussed. Ideas for further development of existing preconditioners are proposed, implemented and investigated numerically.Findings – A two‐level preconditioning, consisting of a transformation of the original system in the first step and subsequent preconditioning of the transformed system is suggested. The GMRES iterative method, which usually performs well when applied to academic problems, showed dissatisfactory performance for the type of industrial flow simulations investigated in this work. It was found that the BiCGStab method performed best in the tests presented here.Research limitations/implications – The iterative solvers considered here were investigated only for a certain class of polymer flows. More detailed studies for...

On Efficiency of Parallel Solvers for the Blood Flow through Aortic Valve

Mathematical modelling of cardiac haemodynamics presents a great challenge to the computational scientists due to numerous numerical issues and required computational resources. In this paper, we study the parallel performance of 3D simulation software for the blood flow through the aortic valve. The fluid flow problem with the open aortic valve leaflets is formulated and solved in parallel. The choice between the segregated and coupled numerical schemes is discussed and investigated. We present and compare the parallel performance results of both types of parallel solvers. We investigate their strong and weak scalability.

A Comparison of Accuracy and Efficiency of Parallel Solvers for Fractional Power Diffusion Problems

In this paper, we construct and investigate parallel solvers for three dimensional problems described by fractional powers of elliptic operators. The main aim is to make a scalability analysis of parallel versions of several state of the art solvers. The originality of this work is that we also consider the accuracy of the selected numerical algorithms. For comparison of accuracy, we use solutions obtained solving the test problem by the Fourier algorithm. Such analysis enables to compare the efficiency of the proposed parallel algorithms depending on the required accuracy of solution and on a number of processes used in computations.