Consistent Metrics for Code Verification

Kamm, James R.; Rider, William J.; Brock, Jerry S.

doi:10.2172/810093

Cited by 7 publications

(4 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hence, the problem may not be ideal for computing the rate of convergence. Interested readers may refer to for performing convergence analysis in the context of unstructured and (solution‐based) adaptively refined grids.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Hence, the problem may not be ideal for computing the rate of convergence. Interested readers may refer to [71][72][73] for performing convergence analysis in the context of unstructured and (solution-based) adaptively refined grids. In Table V, the average density and the corresponding percentage error estimated for the shell are displayed.…”

Section: Grid Convergence Analysis For the Plastic Collapse Of Cylindmentioning

confidence: 99%

See 1 more Smart Citation

A finite volume cell‐centered Lagrangian hydrodynamics approach for solids in general unstructured grids

Sambasivan

Shashkov

Burton

2013

Numerical Methods in Fluids

View full text Add to dashboard Cite

SUMMARYA finite volume cell‐centered Lagrangian hydrodynamics approach, formulated in Cartesian frame, is presented for solving elasto‐plastic response of solids in general unstructured grids. Because solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum, and energy conservation laws. The total stress is split into deviatoric shear stress and dilatational components. The dilatational response of the material is modeled using the Mie‐Grüneisen equation of state. A predicted trial elastic deviatoric stress state is evolved assuming a pure elastic deformation in accordance with the hypo‐elastic stress‐strain relation. The evolution equations are advanced in time by constructing vertex velocity and corner traction force vectors using multi‐dimensional Riemann solutions erected at mesh vertices. Conservation of momentum and total energy along with the increase in entropy principle are invoked for computing these quantities at the vertices. Final state of deviatoric stress is effected via radial return algorithm based on the J‐2 von Mises yield condition. The scheme presented in this work is second‐order accurate both in space and time. The suitability of the scheme is evinced by solving one‐ and two‐dimensional benchmark problems both in structured grids and in unstructured grids with polygonal cells. Copyright © 2013 John Wiley & Sons, Ltd.

show abstract

Section: Numerical Examplesmentioning

confidence: 99%

Section: Grid Convergence Analysis For the Plastic Collapse Of Cylindmentioning

confidence: 99%

A finite volume cell‐centered Lagrangian hydrodynamics approach for solids in general unstructured grids

Sambasivan

Shashkov

Burton

2013

Numerical Methods in Fluids

View full text Add to dashboard Cite

show abstract

“…Then, a first order Taylor expansion can be used for the approximation B n,k = B n,kÀ1 + (@B/@T) n,kÀ1 (T n,k À T n,kÀ1 ) from which (T n,k À T n,kÀ1 ) can be eliminated using Eq. (24). The convergence of this modified method for treating the non-linearity of the Planck function may be better compared to the simple iteration method.…”

Section: Discrete Ordinates Methods For Solving the Radiation Transpormentioning

confidence: 95%

“…The asymptotic convergence rate quantifies the convergence properties of the software implementation (code) of a numerical algorithm for solving the discretized forms of continuum equations [24].…”

Section: Asymptotic Convergence Analysis Of the Codementioning

confidence: 99%