A TWO-DIMENSIONAL METHOD OF MANUFACTURED SOLUTIONS BENCHMARK SUITE BASED ON VARIATIONS OF LARSEN'S BENCHMARK WITH ESCALATING ORDER OF SMOOTHNESS OF THE EXACT SOLUTION

Conference · Sun May 01 04:00:00 EDT 2011

OSTI ID:1016190

Schunert, Sebastian; Azmy, Yousry Y

The quantification of the discretization error associated with the spatial discretization of the Discrete Ordinate(DO) equations in multidimensional Cartesian geometries is the central problem in error estimation of spatial discretization schemes for transport theory as well as computer code verification. Traditionally fine mesh solutions are employed as reference, because analytical solutions only exist in the absence of scattering. This approach, however, is inadequate when the discretization error associated with the reference solution is not small compared to the discretization error associated with the mesh under scrutiny. Typically this situation occurs if the mesh of interest is only a couple of refinement levels away from the reference solution or if the order of accuracy of the numerical method (and hence the reference as well) is lower than expected. In this work we present a Method of Manufactured Solutions (MMS) benchmark suite with variable order of smoothness of the underlying exact solution for two-dimensional Cartesian geometries which provides analytical solutions aver- aged over arbitrary orthogonal meshes for scattering and non-scattering media. It should be emphasized that the developed MMS benchmark suite first eliminates the aforementioned limitation of fine mesh reference solutions since it secures knowledge of the underlying true solution and second that it allows for an arbitrary order of smoothness of the underlying ex- act solution. The latter is of importance because even for smooth parameters and boundary conditions the DO equations can feature exact solution with limited smoothness. Moreover, the degree of smoothness is crucial for both the order of accuracy and the magnitude of the discretization error for any spatial discretization scheme.

• Research Organization: Idaho National Laboratory (INL)
• Sponsoring Organization: DOE - NE
• DOE Contract Number: AC07-05ID14517
• OSTI ID: 1016190
• Report Number(s): INL/CON-11-21644
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ACCURACY
ANALYTICAL SOLUTION
BENCHMARKS
BOUNDARY CONDITIONS
COMPUTER CODES
Code Verification
EXACT SOLUTIONS
Error Estimation
Larsen's Benchmark
MMS
ROUGHNESS
SCATTERING
TRANSPORT THEORY
VERIFICATION