paper review

[stebiondi]

statement of need

• line 27: Shall you consider "low Mach - incompressible" instead of "low-speed". Low speed could be relatively ambiguous.
• "potential flow solvers offer a computationally and time-saving efficient alternative to high-fidelity computational fluid dynamics (CFD) and experimental approaches": How much? Do you have an order of magnitude? Maybe a citation would help. Also I would reword as computationally efficient as it suppose time saving.

methods

• line 76 maybe explaining it in phi terms: (boundary: n * [grad(phi) - V_body] = 0 where V_ body is the velocity of the airfoil. In this case you would have n*grad(phi) = n * V_body for a moving foil and n * grad(phi) = 0 otherwise
• line 83 "under quasi-steady assumptions" - I believe this is a mistake. Isn't the solver based on unsteady formulation? "unsteady boundary-integral formulation" should be more correct.
• line 110 Add just a short phrase that include the set of n+1 equations used for the n+1 unknowns (those are clear) before citing the external methodology and Kutta + Kelvin. Useful for the reader.
• link the two equations written in the Kutta Condition . How did you move from one to the other? Why are those the same equation?
• line 120 be consistent with notation. I refer to [P] and [P]
• line 144 "ciruclation" - just a typo

[coding4Acause]

Statement of need:

comment-1

• line 27: Shall you consider "low Mach - incompressible" instead of "low-speed". Low speed could be relatively ambiguous.

response -

PANKH/JOSS/paper.md

Line 36 in 460c01d

For low-Mach, incompressible applications—where viscous phenomena are largely confined to thin boundary layers and wakes—potential-flow solvers provide a computationally efficient alternative to high-fidelity CFD. Representative studies and benchmarks report computational cost reductions varying from tens to several orders of magnitude depending on solver formulation and problem size [@katz2001low;@dimitri;@persson2012numerical]. Narrowing down to the case of a pitching and plunging airfoil, PANKH demonstrated a runtime reduction on the order $10^3$ compared to the commercial package ANSYS, when executed on identical single-core hardware. High-fidelity CFD simulations, executed on high-performance computing (HPC) clusters comprising multiple nodes and cores, often demand days of runtime due to their intensive computational requirements and parallel processing across distributed architectures. Experimental aerodynamic investigations, on the other hand, involve considerable capital investment and extended timelines. Designing wind/water tunnel setups, procuring flow visualization tools, and conducting controlled tests may take several months to years. Moreover, accommodating different flow conditions often requires substantial modifications to the experimental apparatus. To mitigate these limitations, scaling laws and dimensional analysis are commonly used but come with their own assumptions and constraints. In contrast, PANKH is a modular and open-source aerodynamic solver written in C++. It is designed to offer a rapid and accessible alternative for potential flow analysis in low-speed aerodynamic applications. Although still in its early development stage, PANKH is capable of delivering accurate estimates of aerodynamic loads within minutes. It runs efficiently even on standard single-core desktop systems. Future enhancements of the software will include parallelization via OpenMP or MPI, significantly improving performance for large-scale unsteady simulations. Additionally, the planned development of a graphical user interface (GUI) will streamline usability across platforms, including Android-based systems, transforming PANKH into a portable and interactive educational tool for both undergraduate and graduate-level aerodynamics courses.

comment-2

• "potential flow solvers offer a computationally and time-saving efficient alternative to high-fidelity computational fluid dynamics (CFD) and experimental approaches": How much? Do you have an order of magnitude? Maybe a citation would help. Also I would reword as computationally efficient as it suppose time saving.

response -

PANKH/JOSS/paper.md

Line 36 in 460c01d

For low-Mach, incompressible applications—where viscous phenomena are largely confined to thin boundary layers and wakes—potential-flow solvers provide a computationally efficient alternative to high-fidelity CFD. Representative studies and benchmarks report computational cost reductions varying from tens to several orders of magnitude depending on solver formulation and problem size [@katz2001low;@dimitri;@persson2012numerical]. Narrowing down to the case of a pitching and plunging airfoil, PANKH demonstrated a runtime reduction on the order $10^3$ compared to the commercial package ANSYS, when executed on identical single-core hardware. High-fidelity CFD simulations, executed on high-performance computing (HPC) clusters comprising multiple nodes and cores, often demand days of runtime due to their intensive computational requirements and parallel processing across distributed architectures. Experimental aerodynamic investigations, on the other hand, involve considerable capital investment and extended timelines. Designing wind/water tunnel setups, procuring flow visualization tools, and conducting controlled tests may take several months to years. Moreover, accommodating different flow conditions often requires substantial modifications to the experimental apparatus. To mitigate these limitations, scaling laws and dimensional analysis are commonly used but come with their own assumptions and constraints. In contrast, PANKH is a modular and open-source aerodynamic solver written in C++. It is designed to offer a rapid and accessible alternative for potential flow analysis in low-speed aerodynamic applications. Although still in its early development stage, PANKH is capable of delivering accurate estimates of aerodynamic loads within minutes. It runs efficiently even on standard single-core desktop systems. Future enhancements of the software will include parallelization via OpenMP or MPI, significantly improving performance for large-scale unsteady simulations. Additionally, the planned development of a graphical user interface (GUI) will streamline usability across platforms, including Android-based systems, transforming PANKH into a portable and interactive educational tool for both undergraduate and graduate-level aerodynamics courses.

Methodology

comment-1

• line 76 maybe explaining it in phi terms: (boundary: n * [grad(phi) - V_body] = 0 where V_ body is the velocity of the airfoil. In this case you would have n*grad(phi) = n * V_body for a moving foil and n * grad(phi) = 0 otherwise

response -

PANKH/JOSS/paper.md

Lines 72 to 76 in 460c01d

	\left[(\nabla \Phi-{\boldsymbol V_{\text{body}}})_i\cdot \hat{\boldsymbol{n}}_i \right]_{t_k} = 0, \quad (1 \leq i \leq n-1)
	$$
	Here, $\Phi$ is the total velocity potential, composed of the perturbation and freestream components, i.e., $\Phi=\Phi_{\text{perturbation}}+\Phi_\infty$. The perturbation potential $\Phi_{\text{perturbation}}$ accounts for the influence of both bound and wake vortices, while $\Phi_{\infty}$ represents the freestream velocity potential. The same equation can be equivalently expressed explicity in terms of velocity as follows:
	$$
	\left[ \left( \boldsymbol{V}_{\text{bound}} + \boldsymbol{V}_{\text{wake}} + \underbrace{\left( \boldsymbol{V}_{\infty} - \overbrace{\left( \boldsymbol{V}_{0} + \boldsymbol{\Omega} \times \boldsymbol{r}_{i} \right)}^{\boldsymbol{V}_{\text{body}}} \right)}_{\boldsymbol{V}_{\text{kinematics}}} \right) \cdot \hat{\boldsymbol{n}}_{i} \right]_{t_k} = 0, \quad (1 \leq i \leq n-1)

The explanation of the no-penetration boundary condition is first expressed in terms of $\Phi$, as you mentioned, then it is expressed explicitly in terms of velocity in the next line.

comment-2

• line 83 "under quasi-steady assumptions" - I believe this is a mistake. Isn't the solver based on unsteady formulation? "unsteady boundary-integral formulation" should be more correct.

response -
Yes, it was a mistake from my side; it has been rectified.

comment-3

• line 110 Add just a short phrase that include the set of n+1 equations used for the n+1 unknowns (those are clear) before citing the external methodology and Kutta + Kelvin. Useful for the reader.

response -

PANKH/JOSS/paper.md

Line 67 in 460c01d

Accordingly, a system of $n+1$ equations is required to determine the $n+1$ unknowns. The following section describes the formulation of these $n+1$ equations in detail.

comment-4

• link the two equations written in the Kutta Condition . How did you move from one to the other? Why are those the same equation?

response -

PANKH/JOSS/paper.md

Lines 99 to 100 in 460c01d

	\gamma_{\text{TE}}(t_k) = 0, \quad \text{where} \quad
	\gamma_{\text{TE}}(t_k) = \gamma_1(t_k) + \gamma_n(t_k) + \gamma_{wp}(t_k)

The expression for $\gamma_{TE}$ in terms of $\gamma_1$ , $\gamma_n$, and $\gamma_{wp}$ is directly merged in the main expression of Kutta condition, i.e, $\gamma_{TE}=0$.

comment-5

• line 120 be consistent with notation. I refer to [P] and [P]

response - Thanks for pointing this out, it has been rectified now.

comment-6

• line 144 "ciruclation" - just a typo

response - Thanks for noting it. It has been rectified.

Thank you again for your valuable input. I hope your concerns have been addressed. I will be happy to resolve any further issues.