This manuscript tackles an important numerical difficulty in geodynamic modelling: the development of uneven tracer distributions during Lagrangian particle advection. The authors propose a tracer-nudging algorithm, derived from the requirement that material density remain constant, which iteratively redistributes tracers until a uniform spatial density is achieved. The idea is elegant and, if widely adopted, could mitigate one of the longest-standing practical problems in high-resolution mantle-convection and lithosphere-deformation studies. While I acknowledge the novelty and potential impact of the work, several aspects of the presentation and validation need to be strengthened before the paper is suitable for publication.

Major comments

1. Demonstrate the method on realistic geodynamic problems
   
   The manuscript shows simple circulation tests only. Please include at least one geologically meaningful application—e.g. a high-viscosity-contrast convection benchmark or a 2-D subduction experiment—to illustrate how tracer nudging behaves in complex, time-dependent flow fields and when and how often the nudging is needed.

     2. Compare with established schemes

The paper states that the computational cost of  tracer nudging is  small,  yet no comparison is provided. As far as I can see from the manuscript, the additional computational cost is probably higher than the existing remedies that only add a correction items to the velocity interpolation. It would be nice if the author make a comparison with other method and emphasize the advantages (and limitations) of this method

3. Clarify applicability to compressible versus incompressible flow

Lines 34–35 imply the method corrects non-divergence-free advection errors. However, many geodynamic models employ compressible Stokes flow, where ∇·v ≠ 0 by definition.

1. • State explicitly that the current formulation targets incompressible Stokes problems.
   • Discuss whether, and how, the nudging algorithm could be adapted to compressible flow, and what errors might arise if it were used without modification.                                                                                                                                                                                                                                                                                                                                                                                                              4. Streamline the figures
     
     Figures 2 and 3 convey nearly the same information. I suggest keeping the one that best illustrates the tracer-density evolution and moving the other to the supplement or removing it entirely.

• Initialise tracer distribution, rho = rho_0
• Time loop: