One-Dimensional Ablation with Pyrolysis Gas Flow Using Finite Control Volume Procedure

Amar, Adam J.; Blackwell, B.F.; Edwards, Jack R.

doi:10.2514/6.2007-4535

Cited by 30 publications

(43 citation statements)

References 10 publications

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“…This problem has been previously used to verify a thermal response code as outlined by Amar, 15 and it is intended to verify the implementation of the two dimensional nonlinear transient heat conduction terms in the governing equations and their requisite terms for Newton's method. Consider a non-ablating, non-decomposing, two dimensional, uniform density planar slab of equal length and width subject to a constant specified heat flux on one face, x = 0, and adiabatic on the other three faces.…”

Section: Iiia1 Problem Statementmentioning

confidence: 99%

“…In the current study, an alternative approach is considered in which the spatial and temporal orders of accuracy are simultaneously verified. 15 Factoring out a b∆h q from the discretization error gives…”

Section: Verificationmentioning

confidence: 99%

“…13,14 Amar, Blackwell, and Edwards used the CVFEM to solve the coupled energy and gas continuity equations and presented verification studies which proved correct implementation of many of the boundary conditions and terms in the governing equations. [15][16][17] Recently, Dec and Braun presented codes that solve one and three-dimensional ablation problems including pyrolysis gas flow. Dec and Braun used the Galerkin finite element method (FEM) for spatial discretization and use linear elastic mesh motion.…”

Section: Introductionmentioning

confidence: 99%

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Development and Verification of the Charring Ablating Thermal Protection Implicit System Solver

Amar

Calvert

Kirk

2011

49th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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The development and verification of the Charring Ablating Thermal Protection Implicit System Solver is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method with first and second order implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton's method, while the fully implicit linear system is solved with the Generalized Minimal Residual method. Verification results from exact solutions and the Method of Manufactured Solutions are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

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Section: Iiia1 Problem Statementmentioning

confidence: 99%

Section: Verificationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Development and Verification of the Charring Ablating Thermal Protection Implicit System Solver

Amar

Calvert

Kirk

2011

49th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

Self Cite

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“…Matrix A is then easily inverted to find y and z using a modified Thomas Algorithm for a singly bordered tridiagonal system of equations, as the one presented in [9]. Because of the simplicity of vector v, the dot products of Equation (5) are straightforward, and the solution essentially required to solve two singly bordered tridiagonal systems of equations.…”

Section: Comparisonmentioning

confidence: 99%

“…In the algorithm, each one of these operations needs to be kept in memory, in the order they were performed. Since the matrix is now lower triangular, the system can be solved directly for y using a slightly modified version of Thomas' backward substitution, used to solve singly bordered tridiagonal matrices [9].…”

Section: Dual Contracting Gridmentioning

confidence: 99%

Variant of the Thomas Algorithm for opposite‐bordered tridiagonal systems of equations

Martin

Boyd

2008

Numer Methods Biomed Eng

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SUMMARYTo solve tridiagonal systems of linear equations, the Thomas Algorithm is a much more efficient method than, for instance, Gaussian elimination. The algorithm uses a series of elementary row operations and can solve a system of n equations in O(n) operations, instead of O(n 3 ). Many variations of the Thomas Algorithm have been developed over the years to solve very specific near-tridiagonal matrix. However, none of these methods address the situation of a system of linear equations that could easily be solved if elementary operations on columns are applied, instead of elementary operations on rows. The present paper proposes an efficient method that allows the use of elementary column operations to solve linear systems of equations using vector multiplication techniques, such as the one proposed by Thomas.

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Numerical algorithms for the determinants of opposite-bordered and singly-bordered tridiagonal matrices

Jia

2020

J Math Chem

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One-Dimensional Ablation with Pyrolysis Gas Flow Using Finite Control Volume Procedure

Cited by 30 publications

References 10 publications

Development and Verification of the Charring Ablating Thermal Protection Implicit System Solver

Development and Verification of the Charring Ablating Thermal Protection Implicit System Solver

Variant of the Thomas Algorithm for opposite‐bordered tridiagonal systems of equations

Numerical algorithms for the determinants of opposite-bordered and singly-bordered tridiagonal matrices

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