scholarly journals ANALYSIS OF UPWIND AND HIGH‐RESOLUTION SCHEMES FOR SOLVING CONVECTION DOMINATED PROBLEMS IN POROUS MEDIA

2006 ◽  
Vol 11 (4) ◽  
pp. 451-474 ◽  
Author(s):  
V. Starikovičius ◽  
R. Čiegis
Keyword(s):  
Porous Media ◽  
High Resolution ◽  
Hyperbolic Equations ◽  
Test Problems ◽  
Differential Approximation ◽  
Upwind Schemes ◽  
High Resolution Schemes ◽  
Differential Approximation Method ◽  
Parallel Arrays ◽  
Convection Dominated

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++ library of parallel arrays ‐ ParSol.

scholarly journals Study on Accuracy of the High-Resolution Schemes

2014 ◽  
Vol 6 ◽  
pp. 905053
Author(s):  
Yawen Tang ◽  
Bo Yu ◽  
Jianyu Xie ◽  
Jingfa Li ◽  
Peng Wang
Keyword(s):  
High Resolution ◽  
Numerical Solution ◽  
Richardson Extrapolation ◽  
Second Order ◽  
Order Accuracy ◽  
Order Of Accuracy ◽  
Numerical Examples ◽  
High Resolution Schemes ◽  
Artificial Diffusion ◽  
Convection Dominated

The high-resolution (HR) schemes have been widely used as they can achieve the numerical solution without oscillation and artificial diffusion, especially for convection-dominated problems. However, there still have arguments about the order of accuracy of HR schemes, especially about the extreme value of the solution. In this paper, it is proved that any HR scheme designed in the NVD diagram has second-order accuracy when its combined segments totally locate in the BAIR region. In other words, it has been verified in our study that the segments, which have low-order accuracy when independently employed, have at least second-order accuracy when locate in BAIR region by analysis of two implementation methods of HR scheme and also a number of numerical examples. Meanwhile Richardson extrapolation has been used to estimate the order of accuracy of HR schemes which achieve the same conclusion.

scholarly journals Comparison of a modified large-particle method with some high resolution schemes. One-dimensional test problems

2019 ◽  
pp. 138-146
Author(s):  
Д.В. Садин ◽  
В.А. Давидчук
Keyword(s):  
High Resolution ◽  
Large Particle ◽  
Particle Method ◽  
Test Problems ◽  
One Dimensional ◽  
Flow Parameters ◽  
Wide Range ◽  
High Resolution Schemes ◽  
Self Similar ◽  
Similar Solutions

Проведен сравнительный анализ вычислительных свойств модифицированного метода крупных частиц на примере одномерных тестовых задач газовой динамики в широком диапазоне параметров течения. Численные результаты сопоставлены с автомодельными решениями и данными, полученными по схемам высокой разрешающей способности от второго до шестого порядков аппроксимации. Представленная схема продемонстрировала вычислительную эффективность и конкурентоспособность. The paper presents a comparative analysis of the computational properties of a modified large-particle method on one-dimensional gas dynamics test problems in a wide range of flow parameters. The numerical results are compared with self-similar solutions and data obtained by high-resolution schemes from the second to the sixth order of approximation. It is shown that the presented scheme is numerically efficient and competitive.

scholarly journals Comparison of a modified large-particle method with some high resolution schemes. Two-Dimensional test problems

2019 ◽  
pp. 337-345
Author(s):  
Д.В. Садин ◽  
Б.В. Беляев ◽  
В.А. Давидчук
Keyword(s):  
High Resolution ◽  
Mach Reflection ◽  
Particle Method ◽  
Test Problems ◽  
Nonlinear Correction ◽  
Smooth Solutions ◽  
High Resolution Schemes ◽  
Double Mach Reflection ◽  
Computational Properties ◽  
Second Order Of Approximation

Исследуются вычислительные свойства предложенной ранее новой модификации метода крупных частиц на основе нелинейной коррекции искусственной вязкости на первом (эйлеровом) этапе и гибридизации потоков на втором (лагранжевом и заключительном) этапе, дополненной двухшаговым алгоритмом РунгеКутты по времени. Метод обладает вторым порядком аппроксимации по пространству и времени на гладких решениях. На примере тестовых задач сверхзвукового потока газа в канале со ступенькой и двойного маховского отражения подтверждена работоспособность и вычислительная эффективность метода в сравнении с современными схемами высокой разрешающей способности. A number of computational properties of the previously proposed new modification of a largeparticle method are studied on the basis of a nonlinear correction of artificial viscosity at the first (Eulerian) stage and a hybridization of fluxes at the second (Lagrangian and final) stage supplemented by a twostep RungeKutta algorithm in time. The method has a second order of approximation in space and time on smooth solutions. The computational efficiency of the method is shown compared to several modern high resolution schemes using the forward facing step problem and the double Mach reflection problem.

The Flow of UCM and Oldroyd-B Fluids Past a Cylinder

2000 ◽  
Author(s):  
Manuel A. Alves ◽  
Fernando T. Pinho ◽  
Paulo J. Oliveira
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
High Resolution ◽  
Constitutive Equations ◽  
Numerical Procedure ◽  
Plane Flow ◽  
Dependent Variables ◽  
High Resolution Schemes ◽  
Structured Meshes ◽  
Volume Method

Abstract Accurate solutions are obtained with the numerical method of Oliveira et al (1998) for the inertialess plane flow around a confined cylinder. This numerical procedure is based on the finite-volume method in non-orthogonal block-structured meshes with a collocated arrangement of the dependent variables, and makes use of a special interpolation practice to avoid stress-velocity decoupling. Two high-resolution schemes are implemented to represent the convective terms in the constitutive equations for the upper converted Maxwell and Oldroyd-B fluids, and the resulting predictions of the drag coefficient on the cylinder are shown to be as accurate as existing finite-element method predictions based on the very accurate h-p refinement technique.

A comparative study of high resolution schemes for solving population balances in crystallization

2006 ◽  
Vol 30 (6-7) ◽  
pp. 1119-1131 ◽  
Author(s):  
S. Qamar ◽  
M.P. Elsner ◽  
I.A. Angelov ◽  
G. Warnecke ◽  
A. Seidel-Morgenstern
Keyword(s):  
High Resolution ◽  
Comparative Study ◽  
High Resolution Schemes ◽  
Population Balances
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