Fluid-Structure Interaction with the Entropic Lattice Boltzmann Method

We propose a novel fluid-structure interaction (FSI) scheme using the entropic multi-relaxation time lattice Boltzmann (KBC) model for the fluid domain in combination with a nonlinear finite element solver for the structural part. We show validity of the proposed scheme for various challenging set-ups by comparison to literature data. Beyond validation, we extend the KBC model to multiphase flows and couple it with FEM solver. Robustness and viability of the entropic multi-relaxation time model for complex FSI applications is shown by simulations of droplet impact on elastic superhydrophobic surfaces

Exploring shock-capturing schemes for Particles on Demand simulation of compressible flows

In this exploratory study, we apply shock-capturing schemes within the framework of the Particles on Demand kinetic model to simulate compressible flows with mild and strong shock waves and discontinuities. The model is based on the semi-Lagrangian method where the information propagates along the characteristics while a set of shock-capturing concepts such as the total variation diminishing and weighted essentially non-oscillatory schemes are employed to capture the discontinuities and the shock-waves. The results show that the reconstruction schemes are able to remove the oscillations at the location of the shock waves and together with the Galilean invariance nature of the Particles on Demand model, stable simulations of mild to extreme compressible benchmarks can be carried out. Moreover, the essential numerical properties of the reconstruction schemes such as their spectral analysis and order of accuracy are discussed

Multi-resolution lattice Green's function method for incompressible flows

We propose a multi-resolution strategy that is compatible with the lattice Green's function (LGF) technique for solving viscous, incompressible flows on unbounded domains. The LGF method exploits the regularity of a finite-volume scheme on a formally unbounded Cartesian mesh to yield robust and computationally efficient solutions. The original method is spatially adaptive, but challenging to integrate with embedded mesh refinement as the underlying LGF is only defined for a fixed resolution. We present an ansatz for adaptive mesh refinement, where the solutions to the pressure Poisson equation are approximated using the LGF technique on a composite mesh constructed from a series of infinite lattices of differing resolution. To solve the incompressible Navier-Stokes equations, this is further combined with an integrating factor for the viscous terms and an appropriate Runge-Kutta scheme for the resulting differential-algebraic equations. The parallelized algorithm is verified through with numerical simulations of vortex rings, and the collision of vortex rings at high Reynolds number is simulated to demonstrate the reduction in computational cells achievable with both spatial and refinement adaptivity

A fast multi-resolution lattice Green's function method for elliptic difference equations

We propose a mesh refinement technique for solving elliptic difference equations on unbounded domains based on the fast lattice Green's function (FLGF) method. The FLGF method exploits the regularity of the Cartesian mesh and uses the fast multipole method in conjunction with fast Fourier transforms to yield linear complexity and decrease time-to-solution. We extend this method to a multi-resolution scheme and allow for locally refined Cartesian blocks embedded in the computational domain. Appropriately chosen interpolation and regularization operators retain consistency between the discrete Laplace operator and its inverse on the unbounded domain. Second-order accuracy and linear complexity are maintained, while significantly reducing the number of degrees of freedom and hence the computational cost

A fast multi-resolution lattice Green's function method for elliptic difference equations

We propose a mesh refinement technique for solving elliptic difference equations on unbounded domains based on the fast lattice Green's function (FLGF) method. The FLGF method exploits the regularity of the Cartesian mesh and uses the fast multipole method in conjunction with fast Fourier transforms to yield linear complexity and decrease time-to-solution. We extend this method to a multi-resolution scheme and allow for locally refined Cartesian blocks embedded in the computational domain. Appropriately chosen interpolation and regularization operators retain consistency between the discrete Laplace operator and its inverse on the unbounded domain. Second-order accuracy and linear complexity are maintained, while significantly reducing the number of degrees of freedom and hence the computational cost

Control Requirements and Benchmarks for Quantum Error Correction

Reaching useful fault-tolerant quantum computation relies on successfully implementing quantum error correction (QEC). In QEC, quantum gates and measurements are performed to stabilize the computational qubits, and classical processing is used to convert the measurements into estimated logical Pauli frame updates or logical measurement results. While QEC research has concentrated on developing and evaluating QEC codes and decoding algorithms, specification and clarification of the requirements for the classical control system running QEC codes are lacking. Here, we elucidate the roles of the QEC control system, the necessity to implement low latency feed-forward quantum operations, and suggest near-term benchmarks that confront the classical bottlenecks for QEC quantum computation. These benchmarks are based on the latency between a measurement and the operation that depends on it and incorporate the different control aspects such as quantum-classical parallelization capabilities and decoding throughput. Using a dynamical system analysis, we show how the QEC control system latency performance determines the operation regime of a QEC circuit: latency divergence, where quantum calculations are unfeasible, classical-controller limited runtime, or quantum-operation limited runtime where the classical operations do not delay the quantum circuit. This analysis and the proposed benchmarks aim to allow the evaluation and development of QEC control systems toward their realization as a main component in fault-tolerant quantum computation.Comment: 21+9(SM) pages, 6+3(SM) figure