High-resolution multi-domain space–time isogeometric analysis of car and tire aerodynamics with road contact and tire deformation and rotation

Abstract

We are presenting high-resolution space–time (ST) isogeometric analysis of car and tire aerodynamics with near-actual tire geometry, road contact, and tire deformation and rotation. The focus in the high-resolution computation is on the tire aerodynamics. The high resolution is not only in space but also in time. The influence of the aerodynamics of the car body comes, in the framework of the Multidomain Method (MDM), from the global computation with near-actual car body and tire geometries, carried out earlier with a reasonable mesh resolution. The high-resolution local computation, carried out for the left set of tires, takes place in a nested MDM sequence over three subdomains. The first subdomain contains the front tire. The second subdomain, with the inflow velocity from the first subdomain, is for the front-tire wake flow. The third subdomain, with the inflow velocity from the second subdomain, contains the rear tire. All other boundary conditions for the three subdomains are extracted from the global computation. The full computational framework is made of the ST Variational Multiscale (ST-VMS) method, ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods, ST Isogeometric Analysis (ST-IGA), integrated combinations of these ST methods, element-based mesh relaxation (EBMR), methods for calculating the stabilization parameters and related element lengths targeting IGA discretization, Complex-Geometry IGA Mesh Generation (CGIMG) method, MDM, and the “ST-C” data compression. Except for the last three, these methods were used also in the global computation, and they are playing the same role in the local computation. The ST-TC, for example, as in the global computation, is making the ST moving-mesh computation possible even with contact between the tire and the road, thus enabling high-resolution flow representation near the tire. The CGIMG is making the IGA mesh generation for the complex geometries less arduous. The MDM is reducing the computational cost by focusing the high-resolution locally to where it is needed and also by breaking the local computation into its consecutive portions. The ST-C data compression is making the storage of the data from the global computation less burdensome. The car and tire aerodynamics computation we present shows the effectiveness of the high-resolution computational analysis framework we have built for this class of problems.

T-splines computational membrane–cable structural mechanics with continuity and smoothness: I. Method and implementation

“…The letter "C" in "ST-C" means "continuous." This is a method for extracting time-continuous data from the computed data, and it can work as a data compression method in dealing with large data volumes [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. The classes of problems computed by using the ST-IGA with IGA basis functions in time include wind turbines [9,24,25,[30][31][32][33], turbomachinery [7,20,21,24,25,34,35], flapping-wing aerodynamics [6,[10][11][12][13][14][15], spacecraft cover separation aerodynamics [36], and higher-order temporal IGA discretization [37].…”

“…The classes of problems computed by using the ST-IGA with IGA basis functions in space include wind turbines [24][25][26][27][28]32,33], turbomachinery [7,20,21,24,25,34,35], ground vehicles and tires [29,33,[38][39][40][41][42][43], fluid films [40,43,44], parachutes [22,23,45,46], cardiovascular medicine [47][48][49][50][51][52][53][54][55][56][57], Taylor-Couette flow [58], U-ducts [58], higher-order temporal IGA discretization [37], boundary-layer mesh resolution studies [59], and long-wake flows [60].…”