Adaptive volume penalization for ocean modeling

The development of various volume penalization techniques for use in modeling topographical features in the ocean is the focus of this paper. Due to the complicated geometry inherent in ocean boundaries, the stair-step representation used in the majority of current global ocean circulation models causes accuracy and numerical stability problems. Brinkman penalization is the basis for the methods developed here and is a numerical technique used to enforce no-slip boundary conditions through the addition of a term to the governing equations. The second aspect to this proposed approach is that all governing equations are solved on a nonuniform, adaptive grid through the use of the adaptive wavelet collocation method. This method solves the governing equations on temporally and spatially varying meshes, which allows higher effective resolution to be obtained with less computational cost. When penalization methods are coupled with the adaptive wavelet collocation method, the flow near the boundary can be well-resolved. It is especially useful for simulations of boundary currents and tsunamis, where flow near the boundary is important. This paper will give a thorough analysis of these methods applied to the shallow water equations, as well as some preliminary work applying these methods to volume penalization for bathymetry representation for use in either the nonhydrostatic or hydrostatic primitive equations

Simulating water-entry/exit problems using Eulerian-Lagrangian and fully-Eulerian fictitious domain methods within the open-source IBAMR library

In this paper we employ two implementations of the fictitious domain (FD) method to simulate water-entry and water-exit problems and demonstrate their ability to simulate practical marine engineering problems. In FD methods, the fluid momentum equation is extended within the solid domain using an additional body force that constrains the structure velocity to be that of a rigid body. Using this formulation, a single set of equations is solved over the entire computational domain. The constraint force is calculated in two distinct ways: one using an Eulerian-Lagrangian framework of the immersed boundary (IB) method and another using a fully-Eulerian approach of the Brinkman penalization (BP) method. Both FSI strategies use the same multiphase flow algorithm that solves the discrete incompressible Navier-Stokes system in conservative form. A consistent transport scheme is employed to advect mass and momentum in the domain, which ensures numerical stability of high density ratio multiphase flows involved in practical marine engineering applications. Example cases of a free falling wedge (straight and inclined) and cylinder are simulated, and the numerical results are compared against benchmark cases in literature.Comment: The current paper builds on arXiv:1901.07892 and re-explains some parts of it for the reader's convenienc

Immersed boundary methods for numerical simulation of confined fluid and plasma turbulence in complex geometries: a review

Immersed boundary methods for computing confined fluid and plasma flows in complex geometries are reviewed. The mathematical principle of the volume penalization technique is described and simple examples for imposing Dirichlet and Neumann boundary conditions in one dimension are given. Applications for fluid and plasma turbulence in two and three space dimensions illustrate the applicability and the efficiency of the method in computing flows in complex geometries, for example in toroidal geometries with asymmetric poloidal cross-sections.Comment: in Journal of Plasma Physics, 201

A High-Resolution Penalization Method for large Mach number Flows in the presence of Obstacles

International audienceA penalization method is applied to model the interaction of large Mach number compressible flows with obstacles. A supplementary term is added to the compressible Navier-Stokes system, seeking to simulate the effect of the Brinkman-penalization technique used in incompressible flow simulations including obstacles. We present a computational study comparing numerical results obtained with this method to theoretical results and to simulations with Fluent software. Our work indicates that this technique can be very promising in applications to complex flows

Topology Optimization of Convective Cooling System Designs

This research investigates an approach to finding the optimal geometry of convective cooling system structures for the enhancement of cooling performance. To predict the cooling effect of convective heat transfer, flow analysis is performed by solving the Brinkman-penalized Navier-Stokes equation, and the temperature profile is obtained from the homogenized thermal-transport equation. For accurate and cost-effective analysis, stabilized finite element methods (FEM) and the adjoint sensitivity method for the multiphysics system are implemented. Several stabilization methods with different definitions of their stabilization tensors and the Newton-Raphson iteration method are introduced to solve the governing equations. This study investigates numerical instabilities, such as velocity and pressure oscillation at the fluid-solid interfaces, which result from the fact that the non body-conforming mesh for the topology optimization method fails to capture the sharp change in velocity gradient with a high Reynolds number flow. These oscillations are not problematic at the system analysis level, but prevent the design from converging to an optimized shape at the design optimization level, creating element-scale cavities near the solid boundaries. Several stabilization methods are examined for their ability to alleviate the instabilities. The Galerkin/least-square method produces less oscillation in most cases but it is insufficient in resolving the convergence issue. The density and sensitivity filters do not effectively suppress the cavities at the design optimization level, while a move-limit scheme easily prevents this instability without significant increase in computational cost. The topology optimization method is applied to the convective cooling system design, by using the same configuration that was successfully used in designing the Navier-Stokes flow system. The main design purpose is to design a flow channel to maximize cooling efficiency. A numerical issue concerning the behavior of the Brinkman penalization is presented with example designs. The optimizer frequently ignores the Brinkman penalization and creates infeasible designs. To resolve this issue, a multi-objective function that also minimizes pressure drop is suggested. As design examples, 2D and 3D cooling channels are designed by the multi-objective function, and the effect of Reynolds and Prandtl number change is discussed.Ph.D.Mechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91462/1/kjun_1.pd

Penalization modeling of a limiter in the Tokamak edge plasma

International audienceAn original penalization method is applied to model the interaction of magnetically confined plasma with limiter in the frame of minimal transport model for ionic density and parallel momentum. The limiter is considered as a pure particle sink for the plasma and consequently the density and the momentum are enforced to be zero inside. Comparisons of the numerical results with one dimensional analytical solutions show a very good agreement. In particular, presented method provides a plasma velocity which is almost sonic at the boundaries obstacles as expected from the sheath conditions through the Bohm criterion. The new system being solved in an obstacle free domain, an efficient pseudo-spectral algorithm based on a Fast Fourier transform is also proposed, and associated with an exponential filtering of the unphysical oscillations due to Gibbs phenomenon. Finally, the efficiency of the method is illustrated by investigating the flow spreading from the plasma core to the Scrape Off Layer at the wall in a two-dimensional system with one then two limiters neighboring

A conservative coupling algorithm between a compressible flow and a rigid body using an Embedded Boundary method

This paper deals with a new solid-fluid coupling algorithm between a rigid body and an unsteady compressible fluid flow, using an Embedded Boundary method. The coupling with a rigid body is a first step towards the coupling with a Discrete Element method. The flow is computed using a Finite Volume approach on a Cartesian grid. The expression of numerical fluxes does not affect the general coupling algorithm and we use a one-step high-order scheme proposed by Daru and Tenaud [Daru V,Tenaud C., J. Comput. Phys. 2004]. The Embedded Boundary method is used to integrate the presence of a solid boundary in the fluid. The coupling algorithm is totally explicit and ensures exact mass conservation and a balance of momentum and energy between the fluid and the solid. It is shown that the scheme preserves uniform movement of both fluid and solid and introduces no numerical boundary roughness. The effciency of the method is demonstrated on challenging one- and two-dimensional benchmarks

Characteristic-Based Volume Penalization Method for Compressible Flow Simulations on Unstructured Meshes

The Characteristic-Based Volume Penalization (CBVP) method for numerical simulations of compressible flow over solid obstacles on unstructured meshes is presented. The approach belongs to the class of immersed boundary methods and is not relying on body-fitted meshes. Characteristic penalization terms, added to the compressible Navier-Stokes equations, are used to impose Dirichlet and Neumann boundary conditions on solid-fluid interface with an a priori defined accuracy. The details of numerical implementation, utilizing hybrid finitevolume method with high order edge-based reconstruction schemes in the flow region and loworder finite-difference approximation inside of the obstacle, are discussed. The developed algorithm provides the ability to perform calculations on grids of arbitrary type, including fully unstructured meshes. The efficiency of the characteristic based volume penalization method and its numerical implementation is demonstrated for shock wave reflection, acoustic pulse reflection and Couette flow problems. The results of CBVP simulations are compared with the numerical solutions of the same problems using Brinkman volume penalization method

Pressure-tight and non-stiff volume penalization for compressible flows

Embedding geometries in structured grids allows a simple treatment of complex objects in fluid simulations. Various methods for embedding geometries are available. The commonly used Brinkman-volume-penalization models geometries as porous media, and approximates a solid object in the limit of vanishing porosity. In its simplest form, the momentum equations are augmented by a term penalizing the fluid velocity, yielding good results in many applications. However, it induces numerical stiffness, especially if high-pressure gradients need to be balanced. Here, we focus on the effect of the reduced effective volume (commonly called porosity) of the porous medium. An approach is derived, which allows reducing the flux through objects to practically zero with little increase of numerical stiffness. Also, non-slip boundary conditions and adiabatic boundary conditions are easily constructed. The porosity terms allow keeping the skew symmetry of the underlying numerical scheme, by which the numerical stability is improved. Furthermore, very good conservation of mass and energy in the non-penalized domain can be achieved, for which the boundary smoothing introduces a small ambiguity in its definition. The scheme is tested for acoustic scenarios, for near incompressible and strongly compressible flows.TU Berlin, Open-Access-Mittel - 2022DFG, 200291049, SFB 1029: TurbIn - Signifikante Wirkungsgradsteigerung durch gezielte, interagierende Verbrennungs- und Strömungsinstationaritäten in Gasturbine