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## Publications

Publications (45)

The flow of an active thermal protection system exploiting subsonic counter-flow jets for wing leading edges of hypersonic vehicles is numerically studied on the basis of the three dimensional Navier-Stokes equations. The coolant air issuing from around the stagnation point as an array of three jets spreads over both the upper and the lower sides o...

An array of subsonic counter-flow jets is studied as an active thermal protection system (TPS) for wing leading edges of hypersonic vehicles. The performance is numerically estimated in the model case of a circular cylinder on the basis of the 2D compressible Navier-Stokes equations. In contrast to a single subsonic jet, an array of jets is robust...

Developed is a high-order accurate shock-capturing scheme for the compressible Euler/Navier–Stokes equations; the formal accuracy is 5th order in space and 4th order in time. The performance and efficiency of the scheme are validated in various numerical tests. The main ingredients of the scheme are nothing special; they are variants of the standar...

Shock-capturing schemes often exhibit anomalous behaviors, such as the
carbuncle phenomenon and the post-shock oscillations, especially in the
hypersonic flow regime. This paper proposes a simple and effective
remedy against these shock instabilities in the case of the kinetic
Lax–Wendroff scheme, where the well-known classic scheme is
reinforced b...

Example code in FORTRAN for link-wise ACM (see http://dx.doi.org/10.1016/j.jcp.2012.04.027), with the possibility to compare it with standard LBM, for lid driven cavity problem.

The Artificial Compressibility Method (ACM) for the incompressible Navier-Stokes equations is (link-wise) reformulated (referred to as LW-ACM) by a finite set of discrete directions (links) on a regular Cartesian mesh, in analogy with the Lattice Boltzmann Method (LBM). The main advantage is the possibility of exploiting well established technologi...

Both the artificial compressibility method and the lattice Boltzmann method
yield the solutions of the incompressible Navier-Stokes equations in the limit
of the vanishing Mach number. The inclusion of the bulk viscosity is one of
the reasons for the success of the lattice Boltzmann method since it removes
quickly the acoustic mode, which inevitabl...

The artificial compressibility method for the incompressible Navier–Stokes equations is revived as a high order accurate numerical method (fourth order in space and second order in time). Similar to the lattice Boltzmann method, the mesh spacing is linked to the Mach number. An accuracy higher than that of the lattice Boltzmann method is achieved b...

The lattice Boltzmann method (LBM) for the incompressible Navier–Stokes (NS) equations and the gas kinetic scheme for the compressible NS equations are based on the kinetic theory of gases. In the latter case, however, it is shown that the kinetic formulation is necessary only in the discontinuous reconstruction of fluid-dynamic variables for shock...

A numerical method solving the Burgers equation via the difiusion equation is pro- posed. The time variation of numerical solution is given by a rational function. The coe-cient of the polynomials in the denominator and numerator are determined by simple algebra. In the case of vanishingly small viscosity, the numerical method becomes shock-capturi...

The essential role of kinetic theory in the numerical methods for the Navier-Stokes equations (compressible and incompressible) is discussed. The easy theory of characteristics for kinetic equations brings about drastic simplification of approximate Riemann solver employed in various shock-capturing schemes. The lattice Boltzmann method is shown to...

The high-resolution scheme for the compressible Navier–Stokes equations developed in Ohwada and Kobayashi [Management of discontinuous reconstruction in kinetic schemes, J. Comput. Phys. 197 (2004) 116–138] is rederived without using any special techniques of kinetic theory. The scheme is simplified and its efficiency is improved by introducing an...

The present paper concerns two aspects for the Burnett equations. First, we are going to theoretically show the consistency between the traditional Chapman–Enskog expansion and the successive approximation for the BGK equation up to the super-Burnett order. Second, we will design a numerical scheme to efficiently solve the Burnett equations. The cu...

The present paper highlights the importance of management of the discontinuous reconstruction in the kinetic schemes for gasdynamic equation systems. Firstly, it is revealed by the analysis of the gas kinetic-BGK scheme [JCP 171 (2001) 289] that a continuous reconstruction created from a discontinuous one is a key to the successful kinetic schemes....

The time step truncation error of the DSMC is examined numerically. Contrary to the claim of [S.V. Bogomolov, U.S.S.R. Comput. Math. Math. Phys., Vol. 28, 79 (1988)] and in agreement with that of [T. Ohwada, J. Compt. Phys., Vol. 139, 1 (1998)], it is demonstrated that the error of the conventional DSMC per time step Δt is not O(Δt
3) but O(Δt
2)....

A deterministic hybrid method is developed on the basis of the BGK equation. The conventional finite difference scheme for the BGK equation is combined with the finite volume method for the NS equation derived from the BGK equation by the Chapman‐Enskog expansion. The numerical test is carried out in the shock tube problem and the leading edge prob...

A nonlinear wave driven by a plane wall oscillating in its normal direction is analyzed numerically on the basis of the Boltzmann equation for hard‐sphere molecules and the Maxwell‐type
boundary condition by using the direct simulation Monte‐Carlo. The computation is carried out for the case where the wall reciprocates with a constant speed. When...

A general method for the construction of kinetic schemes of evolutionary equations is illustrated with the simple example of the linear advection equation, where the role of the collision effect is clarified theoretically and numerically. The application to the compressible Euler equation and Navier–Stokes equation is explained. The theoretical bac...

The accuracy of splitting method is investigated in an abstract Cauchy problem and is shown to be first order in time for general evolutionary equations except for a special case. A general formula for the leading term is obtained. It is also shown as an immediate consequence of the formula that the accuracy is improved from first order to second o...

Numerical schemes for the compressible Navier-Stokes equations (CNSE) are constructed on the basis of the kinetic equation for the Chapman-Enskog NS distribution function the macroscopic variables of which satisfy the CNSE. It is clarified from this approach that the inclusion of the collision effect in the numerical flux improves the accuracy of t...

High accuracy of the time-differencing method for the spatially non-homogeneous Boltzmann equation, recently developed in [T. Ohwada, Journal of Compt. Phys., 139, 1 (1998)] as the second order approximation of the integral form of the equation along its characteristic line, is demonstrated numerically in both deterministic and stochastic computati...

A uniform flow of a gas condensing onto its plane condensed phase (commonly known as the half-space problem of condensation) is considered. The problem is studied analytically on the basis of the Boltzmann equation when the flow is in a transonic region. The paper clarifies the analytical structure of the solution, especially the mechanism by which...

A higher order time differencing method for the spatially nonhomogeneous Boltzmann equation is derived from the integral form of the equation along its characteristic line. Similar to the splitting method, which solves the collisionless equation in the convection step and the spatially homogeneous Boltzmann equation in the collision step, the prese...

Heat flow and temperature and density distributions in a rarefied gas between two parallel plates at rest with different uniform temperatures are analyzed numerically on the basis of the full nonlinear Boltzmann equation for hard-sphere molecules and the Maxwell-type boundary condition by a finite difference method where the collision term is compu...

Shear flow and thermal creep flow (flow induced by the temperature gradient along the boundary wall) of a rarefied gas over a plane wall are considered on the basis of the linearized Boltzmann equation for hard-sphere molecules and the Maxwell-type boundary condition. The problems are analyzed numerically by the finite difference method developed i...

The validity of the linearized Boltzmann equation in describing the behaviour of rarefied gas flows that deviate only slightly from a uniform equilibrium state is discussed on the basis of several numerical examples. Various examples of the above situation are analyzed numerically by the full nonlinear BKW equation and also by its linearized versio...

The validity of the linearized Boltzmann equation in describing the behaviour of rarefied gas flows that deviate only slightly from a uniform equilibrium state is discussed on the basis of several numerical examples. Various examples of the above situation are analyzed numerically by the full nonlinear BKW (BGK) equation and also by its linearized...

The structure of normal shock waves is investigated on the basis of the standard Boltzmann equation for hard‐sphere molecules. This fundamental nonlinear problem in rarefied gas dynamics is analyzed numerically by a newly developed finite‐difference method, where the Boltzmann collision integral is computed directly without using the Monte Carlo me...

The structure of normal shock waves is investigated numerically on the basis of the standard Boltzmann equation for hard-sphere molecules. The velocity distribution function as well as the macroscopic quantities are obtained accurately by a finite difference method where the collision term is computed directly without using the Monte-Carlo techniqu...

The Grad-Hilbert expansion of the Boltzmann equation is obtained up to the second order in the Knudsen number for a hard-sphere molecular gas. The thermal stress slip condition as well as its associate Knudsen-layer correction, which is second order in the Knudsen number, on the fluid-dynamic type equation so derived is obtained for a hard-sphere m...

Studies of rarefied gas dynamics on the basis of the Boltzmann equation are discussed. The numerical analysis of Couette, Poiseuille, and thermal transpiration flows is described. Evaporation and condensation characteristics are investigated.

A rarefied gas between its two parallel plane condensed phases is
considered, and its steady behavior, especially the rate of evaporation
or condensation on the condensed phases and the negative
temperature-gradient phenomenon, is studied numerically on the basis of
the linearized Boltzmann equation for hard-sphere molecules under the
conventional...

The plane Couette flow of a rarefied gas between two parallel plates
with the same temperature is investigated on the basis of the linearized
Boltzmann equation for hard-sphere molecules and the diffuse reflection
boundary condition. The velocity distribution function of the gas
molecules as well as the gas velocity, stress, and heat flow
distribut...

The Poiseuille and thermal transpiration flows of a rarefied gas between two parallel plates are investigated on the basis of the linearized Boltzmann equation for hard-sphere molecules and diffuse reflection boundary condition. The velocity distribution functions of the gas molecules as well as the gas velocity and heat flow profiles and mass flux...

Shear flow and thermal creep flow (flow induced by the temperature gradient along the boundary wall) of a rarefied gas over a plane wall are considered on the basis of the linearized Boltzmann equation for hard‐sphere molecules and diffuse reflection boundary condition. These fundamental rarefied gas dynamic problems, typical half‐space boundary‐va...

The behavior of a semi‐infinite expanse of a gas bounded by its plane condensed phase, where evaporation or condensation is taking place, is considered on the basis of the linearized Boltzmann equation for hard‐sphere molecules. The half‐space boundary‐value problem of the linearized Boltzmann equation for hard‐sphere molecules is solved numericall...

A semi‐infinite expanse of a rarefied gas over a plane wall where there is a constant heat flow normal to the wall from infinity is considered. The behavior of the gas is analyzed numerically by a finite difference method on the basis of the standard linearized Boltzmann equation for hard‐sphere molecules with diffuse reflection at the wall. From t...

Forces acting on heated circular cylinders in a highly rarefied gas are investigated for various arrangements numerically on the basis of the general theory developed by Sone. Especially, with a cylindrical shell as an example, a single uniformly heated nonconvex body in an infinite expanse of the gas is shown to be subject to a force in contrast t...