arXiv subjects

Thomas Rung

Publications and source records attributed to Thomas Rung.

32 records · Page 2Linked to original sources

arXiv2022

Two-Phase Flow Simulations of Surface Waves in Wind-Forced Conditions

The paper is devoted to two-phase flow simulations and investigates the ability of a diffusive interface Cahn-Hilliard Volume-of-Fluid model to capture the dynamics of the air-sea interface at geophysically relevant Reynolds numbers. It employs a hybrid filtered/averaging Improved Detached Eddy Simulation method to model turbulence, and utilizes a continuum model to account for surface tension if the diffuse interface is under-resolved by the grid. A numerical wind-wave tank is introduced to limit computational costs and results obtained for two wind-wave conditions are analyzed in comparison to experimental data at matched Reynolds numbers. The focus of the comparison is on both time-averaged and wave-coherent quantities, and includes pressure, velocity as well as modeled and resolved Reynolds stresses. In general, numerical predictions agree well with the experimental measurements and reproduce many wave-dependent flow features. Reynolds stresses near the water surface are found to be especially important in modulating the critical layer height. It is concluded that the diffusive interface approach proves to be a promising method for future studies of air-sea interface dynamics in geophysically relevant flows.

physics.flu-dyn↗

arXiv2022

Variational Quantum Algorithms for Computational Fluid Dynamics

Quantum computing uses the physical principles of very small systems to develop computing platforms which can solve problems that are intractable on conventional supercomputers. There are challenges not only in building the required hardware, but also in identifying the most promising application areas and developing the corresponding quantum algorithms. The availability of intermediate-scale noisy quantum computers is now propelling the developments of novel algorithms, with applications across a variety of domains, including in aeroscience. Variational quantum algorithms are particularly promising since they are comparatively noise tolerant and aim to achieve a quantum advantage with only a few hundred qubits. Furthermore, they are applicable to a wide range of optimization problems arising throughout the natural sciences and industry. To demonstrate the possibilities for the aeroscience community, we give a perspective on how variational quantum algorithms can be utilized in computational fluid dynamics. We discuss how classical problems are translated into quantum algorithms and their logarithmic scaling with problem size. As an explicit example we apply this method to Burgers' Equation in one spatial dimension. We argue that a quantum advantage over classical computing methods could be achieved by the end of this decade if quantum hardware progresses as currently envisaged and emphasize the importance of joining up development of quantum algorithms with application-specific expertise to achieve real-world impact.

quant-ph↗

arXiv2022

Application of p-Laplacian relaxed steepest descent to shape optimization in two-phase flows

The paper is concerned with the minimal drag problem in shape optimization of merchant ships exposed to turbulent two-phase flows. Attention is directed to the solution of Reynolds Averaged Navier-Stokes equations using a Finite Volume method. Central aspects are the use of a p-Laplacian relaxed steepest descent direction and the introduction of crucial technical constraints to the optimization procedure, i.e. the center of buoyancy and the displacement of the underwater hull. The example included refers to the frequently investigated Kriso container ship (KCS).

math.OC↗

arXiv2022

A Scalable Algorithm for Shape Optimization with Geometric Constraints in Banach Spaces

This work develops an algorithm for PDE-constrained shape optimization based on Lipschitz transformations. Building on previous work in this field, the $p$-Laplace operator is utilized to approximate a descent method for Lipschitz shapes. In particular, it is shown how geometric constraints are algorithmically incorporated avoiding penalty terms by assigning them to the subproblem of finding a suitable descent direction. A special focus is placed on the scalability of the proposed methods for large scale parallel computers via the application of multigrid solvers. The preservation of mesh quality under large deformations, where shape singularities have to be smoothed or generated within the optimization process, is also discussed. It is shown that the interaction of hierarchically refined grids and shape optimization can be realized by the choice of appropriate descent directions. The performance of the proposed methods is demonstrated for energy dissipation minimization in fluid dynamics applications.

math.OC↗

arXiv2022

Discrete Adjoint Momentum-Weighted Interpolation Strategies

This Technical Note outlines an adjoint complement to a critical building block of pressure-based Finite-Volume (FV) flow solvers that employ a collocated variable arrangement to simulate virtually incompressible fluids. The focal point is to strengthen the adjoint pressure-velocity coupling by using an adjoint Momentum-Weighted Interpolation (MWI) strategy. To this end, analogies of established primal MWI techniques are derived and investigated. The study reveals the merits of an adjoint MWI but also highlights the importance of its careful implementation.

math.NA↗

arXiv2022

Adjoint Node-Based Shape Optimization of Free Floating Vessels

The paper is concerned with a node-based, gradient-driven, continuous adjoint two-phase flow procedure to optimize the shapes of free-floating vessels and discusses three topics. First, we aim to convey that elements of a Cahn-Hilliard formulation should augment the frequently employed Volume-of-Fluid two-phase flow model to maintain dual consistency. It is seen that such consistency serves as the basis for a robust primal/adjoint coupling in practical applications at huge Reynolds and Froude numbers. The second topic covers different adjoint coupling strategies. A central aspect of the application is the floating position, particularly the trim and the sinkage, that interact with a variation of hydrodynamic loads induced by the shape updates. Other topics addressed refer to the required level of density coupling and a more straightforward -- yet non-frozen -- adjoint treatment of turbulence. The third part discusses the computation of a descent direction within a node-based environment. We will illustrate means to deform both the volume mesh and the hull shape simultaneously and at the same time obey technical constraints on the vessel's displacement and its extensions. The Hilbert-space approach provides smooth shape updates using the established coding infrastructure of a computational fluid dynamics algorithm and provides access to managing additional technical constraints. Verification and validation follow from a submerged 2D cylinder case. The application includes a full-scale offshore supply vessel at Re=3E+08 and Fn=0.37. Results illustrate that the fully parallel procedure can automatically reduce the drag of an already pre-optimized shape by 9-13 within approximately O(10.000-30.000) CPUh depending on the considered couplings and floatation aspects.

physics.flu-dyn↗

arXiv2021

Free surface flow through rigid porous media -- An overview and comparison of formulations

In many applications free surface flow through rigid porous media has to be modeled. Examples refer to coastal engineering applications as well as geotechnical or biomedical applications. Albeit the frequent applications, slight inconsistencies in the formulation of the governing equations can be found in the literature. The main goal of this paper is to identify these differences and provide a quantitative assessment of different approaches. Following a review of the different formulations, simulation results obtained from three alternative formulations are compared with experimental and numerical data. Results obtained by 2D and 3D test cases indicate that the predictive differences returned by the different formulations remain small for most applications, in particular for small porous Reynolds number ReP < 5000. Thus it seems justified to select a formulation that supports an efficient algorithm and coding structure.

physics.flu-dyn↗

arXiv2021

A Novel $p$-Harmonic Descent Approach Applied to Fluid Dynamic Shape Optimization

We introduce a novel method for the implementation of shape optimziation in fluid dynamics applications, where we propose to use the shape derivative to determine deformation fields with the help of the $p-$ Laplacian for $p > 2$. This approach is closely related to the computation of steepest descent directions of the shape functional in the $W^{1,\infty}-$ topology. Our approach is demonstrated for shape optimization related to drag-minimal free floating bodies. The method is validated against existing approaches with respect to convergence of the optimization algorithm, the obtained shape, and regarding the quality of the computational grid after large deformations. Our numerical results strongly indicate that shape optimization related to the $W^{1,\infty}$-topology -- though numerically more demanding -- seems to be superior over the classical approaches invoking Hilbert space methods, concerning the convergence, the obtained shapes and the mesh quality after large deformations, in particular when the optimal shape features sharp corners.

math.OC↗

arXiv2021

Adjoint-based Shape Optimization for the Minimization of Flow-induced Hemolysis in Biomedical Applications

This paper reports on the derivation and implementation of a shape optimization procedure for the minimization of hemolysis induction in biomedical devices. Hemolysis is a blood damaging phenomenon that may occur in mechanical blood-processing applications where large velocity gradients are found. An increased level of damaged blood can lead to deterioration of the immune system and quality of life. It is, thus, important to minimize flow-induced hemolysis by improving the design of next-generation biomedical machinery. Emphasis is given to the formulation of a continuous adjoint complement to a power-law hemolysis prediction model dedicated to efficiently identifying the shape sensitivity to hemolysis. The computational approach is verified against the analytical solutions of a benchmark problem and computed sensitivity derivatives are validated by a finite differences study on a generic 2D stenosed geometry. The application included addresses a 3D ducted geometry which features typical characteristics of biomedical devices. An optimized shape, leading to a potential improvement in hemolysis induction up to 22%, is identified. It is shown, that the improvement persists for different, literature-reported hemolysis-evaluation parameters.

physics.flu-dyn↗

arXiv2020

Adjoint Complement to the Universal Momentum Law of the Wall

The paper is devoted to an adjoint complement to the universal Law of the Wall (LoW) for fluid dynamic momentum boundary layers. The latter typically follows from a strongly simplified, unidirectional shear flow under a constant stress assumption. We first derive the adjoint companion of the simplified momentum equation, while distinguishing between two strategies. Using mixing-length arguments, we demonstrate that the frozen turbulence strategy and a LoW-consistent (differentiated) approach provide virtually the same adjoint momentum equations, that differ only in a single scalar coefficient controlling the inclination in the logarithmic region. Moreover, it is seen that an adjoint LoW can be derived which resembles its primal counterpart in many aspects. The strategy is also compatible with wall-function assumptions for prominent RANS-type two-equation turbulence models, which ground on the mixing-length hypothesis. As a direct consequence of the frequently employed assumption that all primal flow properties algebraically scale with the friction velocity, it is demonstrated that a simple algebraic expression provides a consistent closure of the adjoint momentum equation in the logarithmic layer. This algebraic adjoint closure might also serve as an approximation for more general adjoint flow optimization studies using standard one- or two-equation Boussinesq-viscosity models for the primal flow. Results obtained from the suggested algebraic closure are verified against the primal/adjoint LoW formulations for both, low- and high-Re settings. Applications included in this paper refer to two- and three-dimensional shape optimizations of internal and external engineering flows. Related results indicate that the proposed adjoint algebraic turbulence closure accelerates the optimization process and provides improved optima in comparison to the frozen turbulence approach.

physics.flu-dyn↗

arXiv2020

Continuous Adjoint Complement to the Blasius Equation

The manuscript is concerned with a continuous adjoint complement to two-dimensional, incompressible, first-order boundary-layer equations for a flat plate boundary-layer. The text is structured into three parts. The first part demonstrates, that the adjoint complement can be derived in two ways, either following a first simplify then derive or a first derive and then simplify strategy. The simplification step comprises the classical boundary-layer (b.-l.) approximation and the derivation step transfers the primal flow equation into a companion adjoint equation. The second part of the paper comprises the analyses of the coupled primal/adjoint b.-l. framework. This leads to similarity parameters, which turn the Partial-Differential-Equation (PDE) problem into a boundary value problem described by a set of Ordinary-Differential-Equations (ODE) and support the formulation of an adjoint complement to the classical Blasius equation. Opposite to the primal Blasius equation, its adjoint complement consists of two ODEs which can be simplified depending on the treatment of advection. It is shown, that the advective fluxes, which are frequently debated in the literature, vanish for the investigated self-similar b.l. flows. Differences between the primal and the adjoint Blasius framework are discussed against numerical solutions, and analytical expressions are derived for the adjoint b.-l. thickness, wall shear stress and subordinated skin friction and drag coefficients. The analysis also provides an analytical expression for the shape sensitivity to shear driven drag objectives. The third part assesses the predictive agreement between the different Blasius solutions and numerical results for Navier-Stokes simulations of a flat plate b.-l. at Reynolds numbers between 1E+03 <= ReL <= 1E+05 .

physics.flu-dyn↗

arXiv2020

Adjoint Complement to the Volume-of-Fluid Method for Immiscible Flows

The paper is concerned with an adjoint complement to the Volume-of-Fluid (VoF) method for immiscible two-phase flows, e.g. air and water, which is widely used in marine engineering due to its computational efficiency. The particular challenge of the primal and the corresponding adjoint VoF-approach refers to the sharp interface treatment featuring discontinuous physical properties. Both the continuous adjoint two-phase system (integration-by-parts) and the corresponding dual compressive convection schemes (summation-by-parts) are derived for two prominent compressive convection schemes, namely the High Resolution Interface Capturing Scheme (HRIC) and Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM). The dual scheme rigorously mirrors the primal Normalized-Variable-Diagram (NVD) stencils. Attention is restricted to steady state applications. Thus both the primal and the dual procedures are performed in pseudo time and the backward integration of the dual approach is performed around the (pseudo-temporal) converged primal field. The paper analyses the primal and adjoint equations for an engineering model problem. An analytical solution to the model problem is initially presented, which displays that the adjoint part does not offer a unique, non-trivial solution. As a remedy, an additional diffusive concentration term is introduced to the adjoint concentration equation. Numerical results obtained from the modified approach are benchmarked against the analytical solution for the model problem. Supplementary, the influence of the modification on the sensitivities obtained from simulations for the two-dimensional flow around a submerged hydrofoil are discussed. The final application refers to a shape-optimization of a generic 3D underwater vehicle and underlines a negligible influence of the free mobility parameter.

physics.flu-dyn↗

arXiv2020

Cahn-Hilliard Navier-Stokes Simulations for Marine Free-Surface Flows

The paper is devoted to the simulation of maritime two-phase flows of air and water. Emphasis is put on an extension of the classical Volume-of-Fluid (VoF) method by a diffusive contribution derived from a Cahn-Hilliard (CH) model and its benefits for simulating immiscible, incompressible two-phase flows. Such flows are predominantly simulated with implicit VoF schemes, which mostly employ heuristic downwind-biased approximations for the concentration transport to mimic a sharp interface. This strategy introduces a severe time step restriction and requires pseudo time-stepping of steady flows. Our overall goal is a sound description of the free-surface region that alleviates artificial time-step restrictions, facilitates an efficient and robust numerical framework and inherently includes surface tension effects when needed. The approach is verified for an analytical Couette-flow example and the bubble formation under the influence of surface tension forces. 2D Validation examples are concerned with laminar standing waves reaching from gravity to capillary scale as well as a submerged hydrofoil flow. The final application refers to the 3D flow around an experimentally investigated container vessel at fixed floatation for Re=1.4E+07 and Fn=0.26. Results are compared with data obtained from VoF approaches, supplemented by analytical solutions and measurements. The study indicates the superior efficiency, resharpening capability and wider predictive realm of the CH-based extension for free surface flows with a confined spatial range of interface Courant numbers.

physics.comp-ph↗

arXiv2019

Decoupling of Control and Force Objective in Adjoint-Based Fluid Dynamic Shape Optimization

We discuss exterior and classical interior alternatives for evaluating fluid flow induced forces on bodies. The discussion aims at a reduction of the total shape derivative, achieved through a decoupling of control and objective in the exterior approach. In this case, geometric as well as convective contributions to the shape derivative vanish. Convective contributions depend on primal physics and may disappear, which is not the case for geometric components. The latter can be interpreted as curvatures immanent to industrial applications. The remaining local derivative of the objective functional can be determined efficiently with an adjoint system, that differs to the classical approach in its boundary conditions only and resembles an ALE strategy. A two-dimensional flow exposed to gravity illustrates the features of the exterior approach, whereby carefully derived derivatives from a second order Finite-Difference study were used to validate the results.

physics.flu-dyn↗