Scaling limits for the solution of Burgers equation are investigated. It is shown that the limiting distribution for the solution of Wick type Burgers equation with Gaussian initial data is the same as that for the solution of Burgers equation with ordinary product calculated in [LPW96].

A variety of numerical techniques have been explored to solve the shallow water equations in real-time simulations for computer graphics applications. However, determining stability a algorithm is complex and involved task when coupled set nonlinear partial differential need be solved. This paper proposes novel simple technique compare relative empirical finite difference (or any grid-based sch...

Scaling limits for the solution of Burgers equation are investigated. It is shown that the limiting distribution for the solution of Wick type Burgers equation with Gaussian initial data is the same as that for the solution of Burgers equation with ordinary product calculated in LPW96].

A two-step interface capturing scheme, implemented within the framework of conservative level set method, is developed in this study to simulate the gas/water two-phase fluid flow. In addition to solving the pure advection equation, which is used to advect the level set function for tracking interface, both nonlinear and stabilized features are taken into account for the level set function so t...

Considering the Cauchy problem for the Korteweg-de Vries-Burgers equation ut + uxxx + ǫ|∂x| u+ (u)x = 0, u(0) = φ, where 0 < ǫ, α ≤ 1 and u is a real-valued function, we show that it is globally well-posed in Hs (s > sα), and uniformly globally well-posed in H s (s > −3/4) for all ǫ ∈ (0, 1). Moreover, we prove that for any T > 0, its solution converges in C([0, T ]; Hs) to that of the KdV equa...

A numerical method in which the Rankine-Hugoniot condition is enforced at the discrete level is developed. The simple format of central discretization in a finite volume method is used together with the jump condition to develop a simple and yet accurate numerical method free of Riemann solvers and complicated flux splittings. The steady discontinuities are captured accurately by this numerical...

We study the large N limit of the Itzykson – Zuber integral and show that the leading term is given by the exponent of an action functional for the complex inviscid Burgers (Hopf) equation evaluated on its particular classical solution; the eigenvalue densities that enter in the IZ integral being the imaginary parts of the boundary values of this solution. We show how this result can be applied...

We develop and compare two approaches for the proper simulation of flow discontinuities. For the filtered evolution equations the solution is smooth and can be solved for by standard difference schemes without special considerations of discontinuities. Both approaches are based on approximate deconvolution of the filtered solution to obtain a sufficiently accurate representation of the smoothed...

We study the relevance of various scalar equations, such as inviscid Burgers’, Korteweg-de Vries (KdV), extended KdV, and higher order equations (of Camassa-Holm type), as asymptotic models for the propagation of internal waves in a two-fluid system. These scalar evolution equations may be justified with two approaches. The first method consists in approximating the flow with two decoupled, cou...