arXiv subjects

Monica Lăcătuş

Publications and source records attributed to Monica Lăcătuş.

4 recordsLinked to original sources

arXiv2026

IGA-LBM: Isogeometric lattice Boltzmann method

The lattice Boltzmann method (LBM) offers intrinsic parallelism and simple boundary treatment, but Cartesian lattices approximate curved boundaries by stair steps, causing spurious forces and boundary-layer errors. We present an isogeometric collocation lattice Boltzmann method (IGA-LBM) that solves the discrete-velocity BGK system in strong form on body-fitted B-spline and NURBS geometries. Distribution functions are collocated at Greville points, advection is evaluated with high-order operators on the exact spline mapping, and time integration uses a four-stage Runge-Kutta scheme. Exact geometric metrics preserve a uniform free stream to machine precision on curved grids while retaining formal accuracy. The analysis recovers the incompressible Navier-Stokes equations with viscosity nu = cs^2 tau and shows that the main isogeometric advantage is exact geometry rather than a new interior stencil. Centered collocation is stabilized by a high-order filter, a physical-node closure restores fourth-order accuracy near clustered walls, and stiff collision limits the explicit step to dt <= 2.785 tau, scaling as O(Re^-1). Tests confirm the predicted accuracy and the O(Ma^2) compressibility floor. Validation covers the Ghia lid-driven cavity, steady and unsteady flow past a circular cylinder, and a body-fitted NACA0012 airfoil. For the cylinder, recirculation length is within about 9 percent and the Strouhal number within about 2.5 percent of reference values; drag is 6-12 percent above consensus and decreases with refinement, with stable wakes up to Re = 1000. For NACA0012 at Re = 500 and 10 degrees incidence, surface pressure and skin friction agree with reference data within a few percent. The method provides a high-order, free-stream-preserving LBM for curved-boundary flows based on exact B-spline and NURBS geometry, with demonstrated accuracy, stability, and geometric fidelity.

math.NA↗

arXiv2026

Reduced basis algorithm for solving nonlinear differential equations on quantum computers

As quantum computing moves toward scientific computing applications, nonlinear differential equations remain a central challenge since quantum evolution is intrinsically linear. In this work, we introduce a reduced basis algorithm (RBA) for polynomial nonlinear ordinary differential equations (ODEs) and spatially discretized partial differential equations (PDEs). After time discretization, the method composes the resulting polynomial update map over $m$ timesteps, identifies the reduced monomial basis appearing in this composed map, and constructs a linear RBA operator whose action recovers the exact $m$-timestep nonlinear dynamics. Thus, at the level of the chosen discrete update rule, the method introduces no additional approximation error beyond the time discretization error. The qubit number requirement is governed by the size of the reduced monomial basis. For an $n$-dimensional polynomial ODE system of degree $p>1$, the lifted register requires at most $q_m^{\mathrm{ODE}} = O(nm\log p)$ qubits in the full basis scenario. For PDEs discretized on $N^D$ grid points, a locality-based construction requires at most $q_m^{\mathrm{PDE}} = O(D\log N + n m^{D+1}\log p)$ qubits. Hence, the dependence on the grid size remains logarithmic, while the nonlinear overhead is controlled by local reduced basis size. The main computational burden is moved from the quantum computer to a classical preprocessing step, where the reduced monomial basis and RBA operator are constructed for the chosen timestep window. Through numerical tests on the Lorenz system and the one-dimensional Burgers equation, we verify that the RBA reproduces the corresponding discrete time nonlinear dynamics exactly, while exposing the trade-off between timestep composition, reduced basis growth, and locality.

math.NA↗

arXiv2025

Surrogate Quantum Circuit Design for the Lattice Boltzmann Collision Operator

This study introduces a framework for learning a low-depth surrogate quantum circuit (SQC) that approximates the nonlinear, dissipative, and hence non-unitary Bhatnagar-Gross-Krook (BGK) collision operator in the lattice Boltzmann method (LBM) for the D2Q9 lattice. By appropriately selecting the quantum state encoding, circuit architecture, and measurement protocol, non-unitary dynamics emerge naturally within the physical population space. This approach removes the need for probabilistic algorithms relying on any ancilla qubits and post-selection to reproduce dissipation, or for multiple state copies to capture nonlinearity. The SQC is designed to preserve key physical properties of the BGK operator, including mass conservation, scale equivariance, and D8 equivariance, while momentum conservation is encouraged through penalization in the training loss. When compiled to the IBM Heron quantum processor's native gate set, assuming all-to-all qubit connectivity, the circuit requires only 724 native gates and operates locally on the velocity register, making it independent of the lattice size. The learned SQC is validated on two benchmark cases, the Taylor-Green vortex decay and the lid-driven cavity, showing accurate reproduction of vortex decay and flow recirculation. While integration of the SQC into a quantum LBM framework presently requires measurement and re-initialization at each timestep, the necessary steps towards a measurement-free formulation are outlined.

quant-ph↗

arXiv2025

Data-Driven RANS Closures Using a Relative Importance Term Analysis Based Classifier for 2D and 3D Separated Flows

This study presents a novel approach for enhancing Reynolds-averaged Navier-Stokes (RANS) turbulence modeling through the application of a Relative Importance Term Analysis (RITA) methodology to develop a new zonally-augmented $k-ω$ SST model. Traditional Linear Eddy Viscosity Models often struggle with separated flows. Our approach introduces a physics-based binary classifier that systematically identifies separated shear layers requiring correction by analyzing the relative magnitudes of terms in the turbulence kinetic energy equation. Using symbolic regression, we develop compact correction terms for Reynolds stress anisotropy and turbulent kinetic energy production. Trained on two-dimensional configurations, our model demonstrates significant improvements in predicting separation dynamics while maintaining baseline performance and fully attached flows. Generalization tests on Ahmed body and Faith Hill three-dimensional configurations confirm robust transferability, establishing an effective methodology for targeted enhancement of RANS predictions in separated flows.

physics.flu-dyn↗