Mathematical Verification Using Prescribed or Manufactured Solutions

Author(s):  
Sam S. Y. Wang ◽  
Yafei Jia
2011 ◽  
Vol 4 (3) ◽  
pp. 2165-2197 ◽  
Author(s):  
D. T. Welling ◽  
J. Koller ◽  
E. Camporeale

Abstract. Model verification, or the process of ensuring that the prescribed equations are properly solved, is a necessary step in code development. Careful, quantitative verification guides users when selecting grid resolution and time step and gives confidence to code developers that existing code is properly instituted. This work introduces the RadBelt radiation belt model, a new, open-source version of the Dynamic Radiation Environment Assimilation Model (DREAM) and uses the Method of Manufactured Solutions (MMS) to quantitatively verify it. Order of convergence is investigated for a plethora of code configurations and source terms. The ability to apply many different diffusion coefficients, including time constant and time varying, is thoroughly investigated. The model passes all of the tests, demonstrating correct implementation of the numerical solver. The importance of DLL and source term dynamics on the selection of time step and grid size is also explored. Finally, an alternative method to apply the source term is examined to illustrate additional considerations required when non-linear source terms are used.


Author(s):  
João Muralha ◽  
Luís Eça ◽  
Christiaan M. Klaij

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.


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

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