scholarly journals Application of the method of manufactured solutions to the verification of a pressure-based finite-volume numerical scheme

2011 ◽  
Vol 51 (1) ◽  
pp. 85-99 ◽  
Author(s):  
João Marcelo Vedovoto ◽  
Aristeu da Silveira Neto ◽  
Arnaud Mura ◽  
Luis Fernando Figueira da Silva
Keyword(s):  
Finite Volume ◽  
Numerical Scheme ◽  
Manufactured Solutions ◽  
Method Of Manufactured Solutions

Finite Volume Particle Method for Incompressible Flows

2014 ◽  
Vol 656 ◽  
pp. 72-80
Author(s):  
Sterian Danaila ◽  
Delia Teleaga ◽  
Luiza Zavalan
Keyword(s):  
Finite Volume ◽  
Meshless Method ◽  
Incompressible Flows ◽  
Particle Method ◽  
Finite Volume Methods ◽  
Particle Methods ◽  
Navier Stokes ◽  
Ansys Fluent ◽  
Manufactured Solutions ◽  
Method Of Manufactured Solutions

This paper presents an application of the Finite Volume Particle Method to incompressible flows. The two-dimensional incompressible Navier-Stokes solver is based on Chorin’s projection method with finite volume particle discretization. The Finite Volume Particle Method is a meshless method for fluid dynamics which unifies advantages of particle methods and finite volume methods in one scheme. The method of manufactured solutions is used to examine the global discretization error and finally a comparison between finite volume particle method simulations of an incompressible flow around a fixed circular cylinder and the numerical simulations with the CFD code ANSYS FLUENT 14.0 is presented.

Discontinuous Solutions Using the Method of Manufactured Solutions on Finite Volume Solvers

AIAA Journal ◽  
2015 ◽  
Vol 53 (8) ◽  
pp. 2369-2378 ◽  
Author(s):  
Benjamin Grier ◽  
Richard Figliola ◽  
Edward Alyanak ◽  
José Camberos
Keyword(s):  
Finite Volume ◽  
Discontinuous Solutions ◽  
Manufactured Solutions ◽  
Method Of Manufactured Solutions

A Finite Volume Analysis of the Thermohydrodynamic Performance of Finite Journal Bearings

1990 ◽  
Vol 112 (3) ◽  
pp. 557-565 ◽  
Author(s):  
T. Han ◽  
R. S. Paranjpe
Keyword(s):  
Finite Volume ◽  
Numerical Scheme ◽  
Reverse Flow ◽  
Journal Bearings ◽  
Simultaneous Solution ◽  
Volume Analysis ◽  
Recirculating Flow ◽  
Supply Pressure ◽  
Good Sample ◽  
Energy Equations

A rigorous thermohydrodynamic (THD) analysis of finite journal bearings has been developed. THD analysis not only allows a more accurate prediction of the bearing performance characteristics, but it also provides the temperature distribution in the bearing. It involves the simultaneous solution of the Reynolds and energy equations and can handle a wide variety of flow situations, including reverse flow, recirculating flow, and cavitation. The overall numerical scheme is based on a fully conservative finite-volume formulation. The calculated results are compared with the published literature. The qualitative agreement is good. Sample calculations for a typical automotive bearing show that the oil supply pressure and supply configuration significantly affect the bearing performance.

scholarly journals Characterization of Simultaneous Evolution of Size and Composition Distributions Using Generalized Aggregation Population Balance Equation

Pharmaceutics ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1152
Author(s):  
Mehakpreet Singh ◽  
Ashish Kumar ◽  
Saeed Shirazian ◽  
Vivek Ranade ◽  
Gavin Walker
Keyword(s):  
Finite Volume ◽  
Balance Equation ◽  
Numerical Scheme ◽  
Population Balance ◽  
Population Balance Equation ◽  
Finite Volume Scheme ◽  
Average Technique ◽  
Volume Scheme ◽  
Density Prediction ◽  
Cell Average

The application of multi-dimensional population balance equations (PBEs) for the simulation of granulation processes is recommended due to the multi-component system. Irrespective of the application area, numerical scheme selection for solving multi-dimensional PBEs is driven by the accuracy in (size) number density prediction alone. However, mixing the components, i.e., the particles (excipients and API) and the binding liquid, plays a crucial role in predicting the granule compositional distribution during the pharmaceutical granulation. A numerical scheme should, therefore, be able to predict this accurately. Here, we compare the cell average technique (CAT) and finite volume scheme (FVS) in terms of their accuracy and applicability in predicting the mixing state. To quantify the degree of mixing in the system, the sum-square χ2 parameter is studied to observe the deviation in the amount binder from its average. It has been illustrated that the accurate prediction of integral moments computed by the FVS leads to an inaccurate prediction of the χ2 parameter for a bicomponent population balance equation. Moreover, the cell average technique (CAT) predicts the moments with moderate accuracy; however, it computes the mixing of components χ2 parameter with higher precision than the finite volume scheme. The numerical testing is performed for some benchmarking kernels corresponding to which the analytical solutions are available in the literature. It will be also shown that both numerical methods equally well predict the average size of the particles formed in the system; however, the finite volume scheme takes less time to compute these results.

Code Verification of a Pressure-Based Solver for Subsonic Compressible Flows

2020 ◽  
Vol 5 (4) ◽  
Author(s):  
João Muralha ◽  
Luís Eça ◽  
Christiaan M. Klaij
Keyword(s):  
Compressible Flow ◽  
Incompressible Flow ◽  
Compressible Flows ◽  
Simple Algorithm ◽  
Code Verification ◽  
Weighted Interpolation ◽  
Number Range ◽  
Flow Solver ◽  
Manufactured Solutions ◽  
Method Of Manufactured Solutions

Abstract Although most flows in maritime applications can be modeled as incompressible, for certain phenomena like sloshing, slamming, and cavitation, this approximation falls short. For these events, it is necessary to consider compressibility effects. This paper presents the first step toward a solver for multiphase compressible flows: a single-phase compressible flow solver for perfect gases. The main purpose of this work is code verification of the solver using the method of manufactured solutions. For the sake of completeness, the governing equations are described in detail including the changes to the SIMPLE algorithm used in the incompressible flow solver to ensure mass conservation and pressure–velocity–density coupling. A manufactured solution for laminar subsonic flow was therefore designed. With properly defined boundary conditions, the observed order of grid convergence matches the formal order, so it can be concluded that the flow solver is free of coding mistakes, to the extent tested by the method of manufactured solutions. The performance of the pressure-based SIMPLE solver is quantified by reporting iteration counts for all grids. Furthermore, the use of pressure–weighted interpolation (PWI), also known as Rhie–Chow interpolation, to avoid spurious pressure oscillations in incompressible flow, though not strictly necessary for compressible flow, does show some benefits in the low Mach number range.

scholarly journals A conservative numerical scheme for Rosenau-RLW equation based on multiple integral finite volume method

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Cui Guo ◽  
Fang Li ◽  
Wenping Zhang ◽  
Yuesheng Luo
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Lagrange Interpolation ◽  
Numerical Scheme ◽  
Multiple Integral ◽  
Third Order ◽  
Unconditionally Stable ◽  
Fully Discrete ◽  
Second Order In Time ◽  
Volume Method

Abstract A multiple integral finite volume method combined and Lagrange interpolation are applied in this paper to the Rosenau-RLW (RRLW) equation. We construct a two-level implicit fully discrete scheme for the RRLW equation. The numerical scheme has the accuracy of third order in space and second order in time, respectively. The solvability and uniqueness of the numerical solution are shown. We verify that the numerical scheme keeps the original equation characteristic of energy conservation. It is proved that the numerical scheme is convergent in the order of $O(\tau ^{2} + h^{3})$ O ( τ 2 + h 3 ) and unconditionally stable. A numerical experiment is given to demonstrate the validity and accuracy of scheme.

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