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Area of Interests

Broad interests within fluid mechanics, flow modeling, high-order numerical methods, and uncertainty quantification:
High-order accurate numerical methods for compressible turbulence
Wall-modeling in large-eddy simulation for realistic high Reynolds number flows
Numerical methods on hierarchical Cartesian grid suitable for exa-scale post-k supercomputers
LES of flow around an aircraft across the whole flight envelope
DNS and physical modeling of supercritical turbulent flows in liquid rocket engine
Aeroacoustics simulation of whole aircraft
Uncertainty quantification in CFD
Magnetohydrodynamics turbulence: Shock waves and Magnetic reconnection
Other past major research topics may be found in Past Major Research

Research Topics

• High-order accurate numerical methods for compressible turbulence: LAD scheme, secondary conservative scheme, DG method
Compressible turbulent flows that interact with shock waves, contact surfaces, material interface and phase changes are key features in many engineering and scientific problems. We have been developing wide range of high-order accurate numerical methods for compressible turbulence, such as localized artificial diffusivity (LAD) method, secondary conservative scheme, discontinuous Galerkin (DG) method, to study compressible fluid mechanics of shock waves, contact surfaces, material interfaces, turbulence and their interactions.
Shock/turbulence interactions
Multicomponent interfacial flows

• Wall-modeling in large-eddy simulation for realistic high Reynolds number flows
High-fidelity numerical simulations have received increased attention in recent years, as a tool to study the flow physics. Its most successful applications, however, have still been for moderate Reynolds numbers due to the computational cost required to resolve the broadband scales of turbulence although many engineering applications are indeed at high Reynolds numbers. We have proposed a simple method to bypass the the inevitable presence of numerical and subgrid modeling errors in the grid points closest to the wall (Phys. Fluids paper (2012)), and then based on that method we proposed a dynamic non-equilibrium wall model where convection and pressure gradient terms are not neglected (Phys. Fluids paper (2013)). We are currently extending these approaches to more practical flows and high heat flux flows.
Kawai and Larsson, Phys. Fluids, 25 (1), 015105 (2013).
Kawai and Larsson, Phys. Fluids, 24 (1), 015105 (2012).
Kawai and Asada, Comput. Fluids, 85, (2013).


• Numerical methods on hierarchical Cartesian grid suitable for exa-scale post-k supercomputer
Our group has been working on MEXT post-K computer project as a social and scientific priority issue 8, Sub-issue D: Research and development of core technologies to innovate aircraft design and operation. Our group specifically works on developing a highly-accurate secondary conservative scheme on hierarchical Cartesian grid for the massive-parallel exa-scale post-k supercomputer environment.

• LES of flow around an aircraft across the whole flight envelope: Transonic buffet and stall phenomena
We have been developing a large-eddy simulation (LES) methodology to make the LES as a next generation aircraft aerodynamic design tool to predict the aerodynamics across the whole flight envelope including the boundary of the flight envelope, such as transonic buffet and stall phenomenon, at realistic high Reynolds number conditions. The LES methodology is built based on our achievements of high-order accurate numerical method (LAD approach) and wall-modeling in LES. The present wall-modeled LES successfully predicts the transonic buffet onset and also turbulence statistics without the use of ad hoc corrections, something that existing studies fail to do robustly.
Fukushima and Kawai, AIAA Paper 2017-0495, 2017.

• DNS and physical modeling of supercritical turbulent flows in liquid rocket engine
Unique turbulent heat transfer mechanisms under transcritical and supercritical environments are important phenomena in liquid-rocket engine and high-pressure turbine applications. The mechanisms of turbulent heat transfer across the critical point under transcritical and supercritical environments are investigated by solving compressible Navier-Stokes equations with direct numerical simulations. Here we have been studying the fundamental physics of non-linear interactions between the thermal/transport properties and turbulence in heated turbulent boundary layers under transcritical and supercritical environments, and based on the DNS database we also have been studying RANS modeling of supercritical turbulent flows.
Kawai, Terashima and Negishi, J. Comput. Phys., 300, 2015.
Kawai, AIAA Paper 2016-1934, 2016.

• Uncertainty quantification in CFD
The behaviors of realistic performance of designed vehicles and the underlying physics are not well described by deterministic approaches due to limited information regarding their operating conditions and lack of knowledge about the governing physical laws, physical transport properties, physical models, etc. Thus it is crucial that we understand the intrinsic uncertainties and their influence on the quantities of interest for realistic analyses and design of complex systems. We devised a non-intrusive dynamic adaptive sampling method based on the Kriging-model predictors for accurate and effective uncertainty quantification, and successfully applied to quantify the uncertainty operating conditions in transonic flow around an airfoil. We believe that the uncertainty quantification can be an essential part of validation, provide a rigorous measure of confidence, indicate sensitivities and priorities, support fine understanding of physics and physical model development, and also contribute to perform robust design and optimization.
Uncertainty quantification of transonic airfoil under uncertainty in freestream Mach number.
Kawai and Shimoyama, AIAA Paper 2014-2737, 2014.
Shimoyama, Kawai and Alonso, AIAA Paper 2013-1470, 2013.

• Magnetohydrodynamics turbulence: shock waves and magnetic reconnection
Understanding the magnetohydrodynamics (MHD) of compressible flows is a topic of interest for a wide range of research fields, including astrophysics, magnetospheric and heliospheric physics, and engineering. A significant challenge in the field of compressible MHD simulations is to construct a numerical method that is high-order accurate and simultaneously captures shock waves while numerically satisfying the physical constraint of a divergence-free magnetic field. We proposed a new high-order numerical algorithm for compressible MHD flows that inherently maintains a divergence-free magnetic field, while robustly capturing shocks (Kawai, J. Comput. Phys. 2013). This method is now used to study turbulent magnetic reconnection in magnetospheric plasma physics.
Orszag-Tang MHD shock-vortex interaction:
left, temperature; right, div. of magnetic fields
Fast magnetic reconnection
Kawai, J. Comput. Phys., 251, 2013.

Past Research Topics

Past major research topics may be found in Past Major Research