Filtration processes play an important role in a wide range of environmental and industrial applications, including air purification and water treatment. In view of increasing environmental pollution and rising energy demands, filter systems must offer high separation efficiency at low pressure losses and a long operating life. Although modern filter materials and structures are already cost-effective and widely used, their performance often results from empirical design and incremental improvements. As a consequence, filters may be oversized to ensure adequate separation performance, leading to unnecessary pressure losses and thus increased energy consumption during operation. An application-specific filter design, therefore, offers significant potential for energy savings and performance improvements.

Numerical flow simulations provide valuable insights into the flow behavior within and around filter structures and are increasingly being used to support filter development. However, direct simulation of particle deposition using Lagrange or DEM approaches remains computationally intensive and limits their applicability in iterative design and optimization processes. This is particularly critical when comparing multiple geometries or when integrating deposition-related objectives into gradient-based optimization frameworks. To close this gap, a flow-based surrogate approach has been developed.

The proposed surrogate model is based on local flow and surface metrics that are already available from Eulerian steady-state CFD simulations. Instead of explicitly calculating particle trajectories, the approach evaluates deposition tendencies using physically motivated indicators derived from the interaction between the local flow direction, surface orientation, and flow properties near the wall. This formulation enables a continuous, surface-resolved representation of deposition tendencies and avoids the need for stochastic particle simulation using computationally intensive multiphase models. The most important advantages of this approach include:

• Negligible additional computing costs compared to pure flow simulations
• Local and surface-resolved evaluation of deposition tendencies
• Compatibility with adjoint-based sensitivity analysis
• Suitability for comparative geometry evaluation and design screening

The surrogate approach is demonstrated in a parametric study covering variations in particle size, particle density, flow velocity, and filter fibre diameter. The resulting surrogate trends are systematically compared with particle-resolved Lagrangian deposition results to evaluate the consistency, applicability, and limitations of the approach...