arXiv subjects

Martin Isoz

Publications and source records attributed to Martin Isoz.

5 recordsLinked to original sources

arXiv2026

Adaptation of the hybrid fictitious domain-immersed boundary method for Reynolds-averaged turbulence modeling

Engineering practice often calls for shape or topology optimization (TO) of fluid defining components, while the ever-increasing computing power allows the optimized cost functions to be based on computational fluid dynamics (CFD). However, a common bottleneck in CFD-based TO frameworks is the requirement for frequent remeshing. In order to alleviate this bottleneck, we propose an adaptation of an immersed boundary (IB) method variant, the hybrid fictitious domain-immersed boundary method, to leverage Reynolds-averaged Navier-Stokes (RANS) equations and wall function. The main contribution of the present work lies in the design and open-source implementation of the IB-aware steady-state solution of the RANS equations via the SIMPLE algorithm in the OpenFOAM library. For the most common two-equation RANS models, Reynolds numbers from $10^1$ to $10^6$, and several benchmarks, such as flow over a backwards facing step or an Ahmed body, the framework gives results consistent with the standard body-fitted CFD. Furthermore, given the intended application in TO, special emphasis is placed on the robustness and applicability of the approach to general geometries, which is tested on a NACA profile under various angles of attack.

cs.CE↗

arXiv2026

Sequential topology optimization: SIMP initialization for level-set boundary refinement

Density-based topology optimization methods such as SIMP enable efficient topological exploration but produce diffuse material boundaries that require interpretation before manufacturing. Level-set methods maintain sharp interfaces but are sensitive to the initial design. This paper presents a sequential framework that addresses these complementary limitations through a signed distance function (SDF)-based geometry transfer, formulated for three-dimensional meshes. The SIMP density distribution is converted into an SDF that initializes subsequent level-set boundary refinement. From the level-set perspective, the SIMP-derived initialization mitigates sensitivity to the initial design. From the SIMP perspective, the level-set stage acts as optimization-driven post-processing that produces manufacturing-ready boundaries. Validation on three-dimensional cantilever and MBB benchmarks demonstrates compliance comparable to standalone level-set optimization, with up to 4.6x wall-clock speedup on the cantilever case. The full implementation is released under an open-source license to support reproducibility.

cs.CE↗

arXiv2026

A Fast Spectral Formulation of the Multiscale Proper Orthogonal Decomposition

Multiscale Proper Orthogonal Decomposition (mPOD) decomposes fluid flows into energy-optimal modes within prescribed frequency bands by combining Proper Orthogonal Decomposition with a multiresolution analysis (MRA). In its classical formulation, mPOD relies on a filter bank of finite impulse response (FIR) filters, enabling lossless reconstruction while mitigating Gibbs oscillations and temporal ringing. However, the smooth transition bands required for this purpose introduce partial spectral overlap between adjacent scales and require, for each band, the solution of an eigenvalue problem spanning the full temporal dimension. This work introduces a fast spectral formulation of the mPOD that substantially reduces the computational cost. The proposed approach replaces time-domain FIR filters with compact spectral masks enforcing strictly disjoint frequency supports, thereby exactly decoupling the problem across scales. This leads to a block-diagonal correlation operator in spectral space, so that each band can be treated independently. The resulting eigenvalue problems reduce to small systems whose size depends on the number of active frequencies per band rather than the full time dimension. The approach is validated on a synthetic dataset highlighting spectral windowing effects and on experimental particle image velocimetry (PIV) data of a cylinder wake at Reynolds number $\mbox{Re} \approx 5000$. In both cases, the proposed formulation accurately recovers the modal structures and singular values of the classical mPOD while reducing the computational cost by orders of magnitude.

physics.flu-dyn↗

arXiv2025

Smooth geometry extraction from SIMP topology optimization: Signed distance function approach with volume preservation

This paper presents a novel post-processing methodology for extracting high-quality geometries from density-based topology optimization results. Current post-processing approaches often struggle to simultaneously achieve smooth boundaries, preserve volume fraction, and maintain topological features. We propose a robust method based on a signed distance function (SDF) that addresses these challenges through a two-stage process: first, an SDF representation of density isocontours is constructed, which is followed by geometry refinement using radial basis functions (RBFs). The method generates smooth boundary representations that appear to originate from much finer discretizations while maintaining the computational efficiency of coarse mesh optimization. Through comprehensive validation, our approach demonstrates a 18% reduction in maximum equivalent stress values compared to conventional methods, achieved through continuous geometric transitions at boundaries. The resulting implicit boundary representation facilitates seamless export to standard manufacturing formats without intermediate reconstruction steps, providing a robust foundation for practical engineering applications where high-quality geometric representations are essential.

cs.CE↗

arXiv2025

Accelerating shape optimization by deep neural networks with on-the-fly determined architecture

In component shape optimization, the component properties are often evaluated by computationally expensive simulations. Such optimization becomes unfeasible when it is focused on a global search requiring thousands of simulations to be evaluated. Here, we present a viable global shape optimization methodology based on multi-objective evolutionary algorithms accelerated by deep neural networks (DNNs). Our methodology alternates between evaluating simulations and utilizing the generated data to train DNNs with various architectures. When a suitable DNN architecture is identified, the DNN replaces the simulation in the rest of the global search. Our methodology was tested on five ZDT benchmark functions, showing itself at the level of and sometimes more flexible than other state-of-the-art acceleration approaches. Then, it was applied to a real-life optimization problem, namely the shape optimization of a single-phase ejector. Compared with a non-accelerated methodology, ours was able to save weeks of CPU time in solving this problem. To experimentally confirm the performance of the optimized ejector shapes, four of them were 3D printed and tested on the lab scale confirming the predicted performance. This suggests that our methodology could be used for acceleration of other real-life shape optimization problems.

cs.CE↗