Code verification for finite volume multiphase scalar equations using the method of manufactured solutions

2012 ◽  
Vol 231 (7) ◽  
pp. 2924-2944 ◽  
Author(s):  
P.T. Brady ◽  
M. Herrmann ◽  
J.M. Lopez
Keyword(s):  
Finite Volume ◽  
Code Verification ◽  
Manufactured Solutions ◽  
Method Of Manufactured Solutions ◽  
Scalar Equations

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 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

Code verification in computational geomechanics: Method of manufactured solutions (MMS)

2019 ◽  
Vol 116 ◽  
pp. 103178 ◽  
Author(s):  
Arman Khoshghalb ◽  
Omid Ghaffaripour ◽  
Kaveh Zamani ◽  
Arash Tootoonchi
Keyword(s):  
Code Verification ◽  
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.

scholarly journals Rigorous Code Verification: An Additional Tool to Use With the Method of Manufactured Solutions

2019 ◽  
Author(s):  
Aaron M. Krueger ◽  
Vincent A. Mousseau ◽  
Yassin A. Hassan
Keyword(s):  
Exact Solution ◽  
Truncation Error ◽  
Roundoff Error ◽  
Local Truncation Error ◽  
Code Verification ◽  
Order Of Accuracy ◽  
Manufactured Solutions ◽  
Equation Analysis ◽  
Method Of Manufactured Solutions ◽  
Modified Equation

Abstract The Method of Manufactured Solutions (MMS) has proven to be useful for completing code verification studies. MMS allows the code developer to verify that the observed order-of-accuracy matches the theoretical order-of accuracy. Even though the solution to the partial differential equation is not intuitive, it provides an exact solution to a problem that most likely could not be solved analytically. The code developer can then use the exact solution as a debugging tool. While the order-of-accuracy test has been historically treated as the most rigorous of all code verification methods, it fails to indicate code “bugs” that are of the same order as the theoretical order-of-accuracy. The only way to test for these types of code bugs is to verify that the theoretical local truncation error for a particular grid matches the difference between the manufactured solution (MS) and the solution on that grid. The theoretical local truncation error can be computed by using the modified equation analysis (MEA) with the MS and its analytic derivatives, which we call modified equation analysis method of manufactured solutions (MEAMMS). In addition to describing the MEAMMS process, this study shows the results of completing a code verification study on a conservation of mass code. The code was able to compute the leading truncation error term as well as additional higher-order terms. When the code verification process was complete, not only did the observed order-of-accuracy match the theoretical order-of-accuracy for all numerical schemes implemented in the code, but it was also able to cancel the discretization error to within roundoff error for a 64-bit system.

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