Comparison of Spatial Discretization Methods for Solving the SN Equations Using a Three-Dimensional Method of Manufactured Solutions Benchmark Suite with Escalating Order of Nonsmoothness

2015 ◽  
Vol 180 (1) ◽  
pp. 1-29 ◽  
Author(s):  
Sebastian Schunert ◽  
Yousry Azmy
Keyword(s):  
Three Dimensional ◽  
Spatial Discretization ◽  
Discretization Methods ◽  
Manufactured Solutions ◽  
Method Of Manufactured Solutions ◽  
Benchmark Suite

A New Global Spatial Discretization Method for Calculating Dynamic Responses of Two-Dimensional Continuous Systems With Application to a Rectangular Kirchhoff Plate

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
K. Wu ◽  
W. D. Zhu
Keyword(s):  
Boundary Conditions ◽  
Continuous System ◽  
Dynamic Responses ◽  
Kirchhoff Plate ◽  
Continuous Systems ◽  
Discretization Method ◽  
Two Dimensional ◽  
Spatial Discretization ◽  
Arbitrary Boundary ◽  
Discretization Methods

A new global spatial discretization method (NGSDM) is developed to accurately calculate natural frequencies and dynamic responses of two-dimensional (2D) continuous systems such as membranes and Kirchhoff plates. The transverse displacement of a 2D continuous system is separated into a 2D internal term and a 2D boundary-induced term; the latter is interpolated from one-dimensional (1D) boundary functions that are further divided into 1D internal terms and 1D boundary-induced terms. The 2D and 1D internal terms are chosen to satisfy prescribed boundary conditions, and the 2D and 1D boundary-induced terms use additional degrees-of-freedom (DOFs) at boundaries to ensure satisfaction of all the boundary conditions. A general formulation of the method that can achieve uniform convergence is established for a 2D continuous system with an arbitrary domain shape and arbitrary boundary conditions, and it is elaborated in detail for a general rectangular Kirchhoff plate. An example of a rectangular Kirchhoff plate that has three simply supported boundaries and one free boundary with an attached Euler–Bernoulli beam is investigated using the developed method and results are compared with those from other global and local spatial discretization methods. Advantages of the new method over local spatial discretization methods are much fewer DOFs and much less computational effort, and those over the assumed modes method (AMM) are better numerical property, a faster calculation speed, and much higher accuracy in calculation of bending moments and transverse shearing forces that are related to high-order spatial derivatives of the displacement of the plate with an edge beam.

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
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