The Method of Manufactured Solutions in 3D for the verification of Computational Electromagnetics

2012 ◽  
Author(s):  
Renier Marchand ◽  
David B Davidson
Keyword(s):  
Computational Electromagnetics ◽  
Manufactured Solutions ◽  
Method Of Manufactured Solutions

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 Verification of BOUT++ by the method of manufactured solutions

2016 ◽  
Vol 23 (6) ◽  
pp. 062303 ◽  
Author(s):  
B. D. Dudson ◽  
J. Madsen ◽  
J. Omotani ◽  
P. Hill ◽  
L. Easy ◽  
...  
Keyword(s):  
Manufactured Solutions ◽  
Method Of Manufactured Solutions

Code Verification by the Method of Manufactured Solutions

2001 ◽  
Vol 124 (1) ◽  
pp. 4-10 ◽  
Author(s):  
Patrick J. Roache
Keyword(s):  
Solution Structure ◽  
General Procedure ◽  
Grid Refinement ◽  
Complex Solution ◽  
Error Evaluation ◽  
Symbolic Manipulation ◽  
Exact Analytical Solutions ◽  
Manufactured Solutions ◽  
Method Of Manufactured Solutions ◽  
Benchmark Solutions

Verification of Calculations involves error estimation, whereas Verification of Codes involves error evaluation, from known benchmark solutions. The best benchmarks are exact analytical solutions with sufficiently complex solution structure; they need not be realistic since Verification is a purely mathematical exercise. The Method of Manufactured Solutions (MMS) provides a straightforward and quite general procedure for generating such solutions. For complex codes, the method utilizes Symbolic Manipulation, but here it is illustrated with simple examples. When used with systematic grid refinement studies, which are remarkably sensitive, MMS produces strong Code Verifications with a theorem-like quality and a clearly defined completion point.

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