Space-Time Computational Analysis: From Inception to New Generations
Tayfun Tezduyar, Rice University
Space-Time (ST) Variational Multiscale (ST-VMS) method [1] and its predecessor ST-SUPS [2] have a good track record [3] in computational analysis of complex fluid-structure interactions (FSI) and flows with moving boundaries and interfaces (MBI). The classes of challenging problems with successful analysis range from spacecraft parachutes to flow-driven string dynamics in pumps, from stent-treated patient-specific cerebral aneurysms to heart valves, from turbocharger turbines and exhaust manifolds to tire-aerodynamics with actual tire geometry, road contact and tire deformation. When an FSI or MBI problem requires high-resolution representation of boundary layers, ALE and ST methods, where the mesh moves to follow the fluid–solid interface, meet that requirement. Moving-mesh methods have been practical in more classes of complex FSI and MBI problems than commonly thought of. With a number of complementary methods [4, 5, 6, 7] introduced in recent years, the ST methods can now do even more (see, for example, [8, 9]). We provide an overview of how the ST methods started, how they evolved over the years, and the classes of challenging problems that can now be solved.
References
[1] K. Takizawa and T.E. Tezduyar, "Multiscale Space-Time Fluid-Structure Interaction Techniques", Computational Mechanics, 48 (2011) 247-267.
[2] T.E. Tezduyar, "Computation of Moving Boundaries and Interfaces and Stabilization Parameters", International Journal for Numerical Methods in Fluids, 43 (2003) 555-575.
[3] T.E. Tezduyar and K. Takizawa, "Space-Time Computations in Practical Engineering Applications: A Summary of the 25-Year History", Computational Mechanics, 63 (2019) 747-753.
[4] K. Takizawa, T.E. Tezduyar, A. Buscher and S. Asada, "Space-Time Interface-Tracking with Topology Change (ST-TC)", Computational Mechanics, 54 (2014) 955-971.
[5] K. Takizawa, T.E. Tezduyar, H. Mochizuki, H. Hattori, S. Mei, L. Pan and K. Montel, "Space-Time VMS Method for Flow Computations with Slip Interfaces (ST-SI)", Mathematical Models and Methods in Applied Sciences, 25 (2015) 2377-2406.
[6] K. Takizawa, T.E. Tezduyar, S. Asada and T. Kuraishi, "Space-Time Method for Flow Computations with Slip Interfaces and Topology Changes (ST-SI-TC)", Computers & Fluids, 141 (2016) 124-134.
[7] K. Takizawa, T.E. Tezduyar, Y. Otoguro, T. Terahara, T. Kuraishi and H. Hattori, "Turbocharger Flow Computations with the Space-Time Isogeometric Analysis (ST-IGA)", Computers & Fluids, 142 (2017) 15-20.
[8] K. Takizawa, T.E. Tezduyar, T. Terahara and T. Sasaki, "Heart Valve Flow Computation with the Integrated Space-Time VMS, Slip Interface, Topology Change and Isogeometric Discretization Methods", Computers & Fluids, 158 (2017) 176-188.
[9] T. Kuraishi, K. Takizawa and T.E. Tezduyar, "Tire Aerodynamics with Actual Tire Geometry, Road Contact and Tire Deformation", Computational Mechanics, published online, 10.1007/s00466-018-1642-1 (October 2018).
Tayfun Tezduyar, Rice University
Space-Time (ST) Variational Multiscale (ST-VMS) method [1] and its predecessor ST-SUPS [2] have a good track record [3] in computational analysis of complex fluid-structure interactions (FSI) and flows with moving boundaries and interfaces (MBI). The classes of challenging problems with successful analysis range from spacecraft parachutes to flow-driven string dynamics in pumps, from stent-treated patient-specific cerebral aneurysms to heart valves, from turbocharger turbines and exhaust manifolds to tire-aerodynamics with actual tire geometry, road contact and tire deformation. When an FSI or MBI problem requires high-resolution representation of boundary layers, ALE and ST methods, where the mesh moves to follow the fluid–solid interface, meet that requirement. Moving-mesh methods have been practical in more classes of complex FSI and MBI problems than commonly thought of. With a number of complementary methods [4, 5, 6, 7] introduced in recent years, the ST methods can now do even more (see, for example, [8, 9]). We provide an overview of how the ST methods started, how they evolved over the years, and the classes of challenging problems that can now be solved.
References
[1] K. Takizawa and T.E. Tezduyar, "Multiscale Space-Time Fluid-Structure Interaction Techniques", Computational Mechanics, 48 (2011) 247-267.
[2] T.E. Tezduyar, "Computation of Moving Boundaries and Interfaces and Stabilization Parameters", International Journal for Numerical Methods in Fluids, 43 (2003) 555-575.
[3] T.E. Tezduyar and K. Takizawa, "Space-Time Computations in Practical Engineering Applications: A Summary of the 25-Year History", Computational Mechanics, 63 (2019) 747-753.
[4] K. Takizawa, T.E. Tezduyar, A. Buscher and S. Asada, "Space-Time Interface-Tracking with Topology Change (ST-TC)", Computational Mechanics, 54 (2014) 955-971.
[5] K. Takizawa, T.E. Tezduyar, H. Mochizuki, H. Hattori, S. Mei, L. Pan and K. Montel, "Space-Time VMS Method for Flow Computations with Slip Interfaces (ST-SI)", Mathematical Models and Methods in Applied Sciences, 25 (2015) 2377-2406.
[6] K. Takizawa, T.E. Tezduyar, S. Asada and T. Kuraishi, "Space-Time Method for Flow Computations with Slip Interfaces and Topology Changes (ST-SI-TC)", Computers & Fluids, 141 (2016) 124-134.
[7] K. Takizawa, T.E. Tezduyar, Y. Otoguro, T. Terahara, T. Kuraishi and H. Hattori, "Turbocharger Flow Computations with the Space-Time Isogeometric Analysis (ST-IGA)", Computers & Fluids, 142 (2017) 15-20.
[8] K. Takizawa, T.E. Tezduyar, T. Terahara and T. Sasaki, "Heart Valve Flow Computation with the Integrated Space-Time VMS, Slip Interface, Topology Change and Isogeometric Discretization Methods", Computers & Fluids, 158 (2017) 176-188.
[9] T. Kuraishi, K. Takizawa and T.E. Tezduyar, "Tire Aerodynamics with Actual Tire Geometry, Road Contact and Tire Deformation", Computational Mechanics, published online, 10.1007/s00466-018-1642-1 (October 2018).
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