Implicit gradient reconstruction (IGR) method for compressible flow simulation

Singh, Manish K.; Munikrishna, N.; Ramesh, V.; Balakrishnan, N.

doi:10.1088/1742-6596/822/1/012030

Cited by 1 publication

(1 citation statement)

References 6 publications

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“…Preconditioning of A significantly lowers the stiffness by equalizing the eigenvalues of the Jacobian. Singh et al (2017) developed an implicit gradient reconstruction method for compressible flows wherein the eigenvalues of Roe’s Jacobian λ i were scaled using parameters ϕ i . These parameters were determined from the gradients of conserved variables in the upwind cells at an interface, thereby ensuring monotonicity.…”

Section: Introductionmentioning

confidence: 99%

Higher-order implicit shock-capturing scheme based on linearization of implicit fluxes for the Euler equations

Mittakolu

Rani

Sundaram

2023

HFF

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Purpose A higher-order implicit shock-capturing scheme is presented for the Euler equations based on time linearization of the implicit flux vector rather than the residual vector. Design/methodology/approach The flux vector is linearized through a truncated Taylor-series expansion whose leading-order implicit term is an inner product of the flux Jacobian and the vector of differences between the current and previous time step values of conserved variables. The implicit conserved-variable difference vector is evaluated at cell faces by using the reconstructed states at the left and right sides of a cell face and projecting the difference between the left and right states onto the right eigenvectors. Flux linearization also facilitates the construction of implicit schemes with higher-order spatial accuracy (up to third order in the present study). To enhance the diagonal dominance of the coefficient matrix and thereby increase the implicitness of the scheme, wave strengths at cell faces are expressed as the inner product of the inverse of the right eigenvector matrix and the difference in the right and left reconstructed states at a cell face. Findings The accuracy of the implicit algorithm at Courant–Friedrichs–Lewy (CFL) numbers greater than unity is demonstrated for a number of test cases comprising one-dimensional (1-D) Sod’s shock tube, quasi 1-D steady flow through a converging-diverging nozzle, and two-dimensional (2-D) supersonic flow over a compression corner and an expansion corner. Practical implications The algorithm has the advantage that it does not entail spatial derivatives of flux Jacobian so that the implicit flux can be readily evaluated using Roe’s approximate Jacobian. As a result, this approach readily facilitates the construction of implicit schemes with high-order spatial accuracy such as Roe-MUSCL. Originality/value A novel finite-volume-based higher-order implicit shock-capturing scheme was developed that uses time linearization of fluxes at cell interfaces.

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Section: Introductionmentioning

confidence: 99%