What does this research mean for the field?

The Method of Manufactured Solutions (MMS) effectively verifies high-order compact finite-difference schemes for two-dimensional incompressible viscoelastic flows, demonstrating a convergence order of approximately 4.5 across Oldroyd-B and Giesekus constitutive models. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To verify high-order compact finite-difference numerical schemes for two-dimensional incompressible viscoelastic flows formulated in vorticity and stream functions using the Method of Manufactured Solutions.

September 14, 2026International Journal for Numerical Methods in FluidsOpen Access

Verification of an Incompressible Viscoelastic Flow Solver Using the Method of Manufactured Solutions for Oldroyd‐B and Giesekus Constitutive Models

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Authors

JOJuniormar Organista LSLeandro F. Souza CFCélio Fernandes

Discussion

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Overview

Numerical study demonstrates high-order accuracy in viscoelastic flow solvers using manufactured solutions, highlighting a robust verification framework for complex fluid simulations.

Key Points

To verify high-order compact finite-difference numerical schemes for two-dimensional incompressible viscoelastic flows formulated in vorticity and stream functions using the Method of Manufactured Solutions.
Applied the Method of Manufactured Solutions based on a lid-driven cavity benchmark to formulate artificial analytical solutions that preserve boundary conditions and governing equations.
Tested high-order compact finite-difference schemes across Oldroyd-B and Giesekus constitutive models over varying Reynolds numbers, Weissenberg numbers, solvent viscosity ratios, and mobility parameters.
Achieved an asymptotic convergence order of approximately 4.5 for most flow variables across tested parameter spaces.
Vorticity showed slightly reduced convergence orders at higher Reynolds numbers, though mesh refinement consistently reduced global error across both constitutive models.

Cite This Study

Organista et al. (2026) studied this question.

synapsesocial.com/papers/6aa7b3bf0926e14a848b2ee9 https://doi.org/10.1002/fld.70096

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September 14, 2026International Journal for Numerical Methods in FluidsOpen Access

Verification of an Incompressible Viscoelastic Flow Solver Using the Method of Manufactured Solutions for Oldroyd‐B and Giesekus Constitutive Models

View Full Paper

Ask AI

Bookmark

Authors

JOJuniormar Organista LSLeandro F. Souza CFCélio Fernandes

Discussion

Member takes

Overview

Numerical study demonstrates high-order accuracy in viscoelastic flow solvers using manufactured solutions, highlighting a robust verification framework for complex fluid simulations.

Key Points

To verify high-order compact finite-difference numerical schemes for two-dimensional incompressible viscoelastic flows formulated in vorticity and stream functions using the Method of Manufactured Solutions.
Applied the Method of Manufactured Solutions based on a lid-driven cavity benchmark to formulate artificial analytical solutions that preserve boundary conditions and governing equations.
Tested high-order compact finite-difference schemes across Oldroyd-B and Giesekus constitutive models over varying Reynolds numbers, Weissenberg numbers, solvent viscosity ratios, and mobility parameters.
Achieved an asymptotic convergence order of approximately 4.5 for most flow variables across tested parameter spaces.
Vorticity showed slightly reduced convergence orders at higher Reynolds numbers, though mesh refinement consistently reduced global error across both constitutive models.

Cite This Study

Organista et al. (2026) studied this question.

synapsesocial.com/papers/6aa7b3bf0926e14a848b2ee9 https://doi.org/10.1002/fld.70096

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