Computation Of Flow Problems Research Articles

Space–time flow computation with boundary layer and contact representation: a 10-year history

In computation of flow problems with moving solid surfaces, moving-mesh methods such as the space–time (ST) variational multiscale method enable mesh-resolution control near the solid surfaces and thus high-resolution boundary-layer representation. There was, however, a perception that in computations where the solid surfaces come into contact, high-resolution boundary-layer representation and actual-contact representation without leaving a mesh protection opening between the solid surfaces were mutually exclusive objectives in a practical sense. The introduction of the ST topology change (ST-TC) method in 2013 changed the perception. The two objectives were no longer mutually exclusive. The ST-TC makes moving-mesh computation possible even without leaving a mesh protection opening. The contact is represented as an actual contact and the boundary layer is represented with high resolution. Elements collapse or are reborn as needed, and that is attainable in the ST framework while retaining the computational efficiency at a practical level. The ST-TC now has a 10-year history of achieving the two objectives that were long seen as mutually exclusive. With the ST-TC and other ST computational methods introduced before and after, it has been possible to address many of the challenges encountered in conducting flow analysis with boundary layer and contact representation, in the presence of additional intricacies such as geometric complexity, isogeometric discretization, and rotation or deformation of the solid surfaces. The flow analyses conducted with these ST methods include car and tire aerodynamics with road contact and tire deformation and ventricle-valve-aorta flow. To help widen awareness of these methods and what they can do, we provide an overview of the methods, including those formulated in the context of isogeometric analysis, and the computations performed over the 10-year history of the ST-TC.

A linear-elasticity-based mesh moving method with no cycle-to-cycle accumulated distortion

Good mesh moving methods are always part of what makes moving-mesh methods good in computation of flow problems with moving boundaries and interfaces, including fluid–structure interaction. Moving-mesh methods, such as the space–time (ST) and arbitrary Lagrangian–Eulerian (ALE) methods, enable mesh-resolution control near solid surfaces and thus high-resolution representation of the boundary layers. Mesh moving based on linear elasticity and mesh-Jacobian-based stiffening (MJBS) has been in use with the ST and ALE methods since 1992. In the MJBS, the objective is to stiffen the smaller elements, which are typically placed near solid surfaces, more than the larger ones, and this is accomplished by altering the way we account for the Jacobian of the transformation from the element domain to the physical domain. In computing the mesh motion between time levels t_n and t_{n+1} with the linear-elasticity equations, the most common option is to compute the displacement from the configuration at t_n. While this option works well for most problems, because the method is path-dependent, it involves cycle-to-cycle accumulated mesh distortion. The back-cycle-based mesh moving (BCBMM) method, introduced recently with two versions, can remedy that. In the BCBMM, there is no cycle-to-cycle accumulated distortion. In this article, for the first time, we present mesh moving test computations with the BCBMM. We also introduce a version we call “half-cycle-based mesh moving” (HCBMM) method, and that is for computations where the boundary or interface motion in the second half of the cycle consists of just reversing the steps in the first half and we want the mesh to behave the same way. We present detailed 2D and 3D test computations with finite element meshes, using as the test case the mesh motion associated with wing pitching. The computations show that all versions of the BCBMM perform well, with no cycle-to-cycle accumulated distortion, and with the HCBMM, as the wing in the second half of the cycle just reverses its motion steps in the first half, the mesh behaves the same way.

A low-distortion mesh moving method based on fiber-reinforced hyperelasticity and optimized zero-stress state

In computation of flow problems with moving boundaries and interfaces, including fluid–structure interaction, moving-mesh methods enable mesh-resolution control near the interface and consequently high-resolution representation of the boundary layers. Good moving-mesh methods require good mesh moving methods. We introduce a low-distortion mesh moving method based on fiber-reinforced hyperelasticity and optimized zero-stress state (ZSS). The method has been developed targeting isogeometric discretization but is also applicable to finite element discretization. With the large-deformation mechanics equations, we can expect to have a unique mesh associated with each step of the boundary or interface motion. With the fibers placed in multiple directions, we stiffen the element in those directions for the purpose of reducing the distortion during the mesh deformation. We optimize the ZSS by seeking orthogonality of the parametric directions, by mesh relaxation, and by making the ZSS time-dependent as needed. We present 2D and 3D test computations with isogeometric discretization. The computations show that the mesh moving method introduced performs well.

SPACE–TIME VMS METHODS FOR MODELING OF INCOMPRESSIBLE FLOWS AT HIGH REYNOLDS NUMBERS

Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) formulation was developed for flow problems with moving interfaces and has been successfully applied to some of the most complex problems in that category. A new version of the DSD/SST method for incompressible flows, which has additional subgrid-scale representation features, is the space–time version of the residual-based variational multiscale (VMS) method. This new version, called DSD/SST-VMST and also Space–Time VMS (ST-VMS), provides a more comprehensive framework for the VMS method. We describe the ST-VMS method, including the embedded stabilization parameters, and assess its performance in computation of flow problems at high Reynolds numbers by comparing the results to experimental data. The computations, which include those with 3D airfoil geometries and spacecraft configurations, signal a promising future for the ST-VMS method.

Computation of flow problems with the Mixed Interface-Tracking/Interface-Capturing Technique (MITICT)

In computation of flow problems with fluid–solid interfaces, an interface-tracking technique, where the fluid mesh moves to track the interface, would allow us to have full control of the resolution of the fluid mesh in the boundary layers. With an interface-capturing technique (or an interface locator technique in the more general case), on the other hand, independent of how accurately the interface geometry is represented, the resolution of the fluid mesh in the boundary layer will be limited by the resolution of the fluid mesh at the interface. In computation of flow problems with fluid–fluid interfaces where the interface is too complex or unsteady to track while keeping the remeshing frequency under control, interface-capturing techniques, with enhanced-discretization as needed, could be used as more flexible alternatives. Sometimes we may need to solve flow problems with both fluid–solid interfaces and complex or unsteady fluid–fluid interfaces. The Mixed Interface-Tracking/Interface-Capturing Technique (MITICT) was introduced for computation of flow problems that involve both interfaces that can be accurately tracked with a moving mesh method and interfaces that are too complex or unsteady to be tracked and therefore require an interface-capturing technique. As the interface-tracking technique, we use the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) formulation. The interface-capturing technique rides on this, and is based on solving over a moving mesh, in addition to the Navier–Stokes equations, the advection equation governing the time-evolution of the interface function. For the computations reported in this paper, as interface-capturing technique we are using one of the versions of the Edge-Tracked Interface Locator Technique (ETILT).