相关论文: Analytical shock solutions at large and small Pran…
This contribution Part II of a two-part series, extends the general-domain FC-SDNN (Fourier Continuation Shock-Detecting Neural Network) introduces in Part I to enable treatment of non-smooth domains, it introduces a parallel implementation…
A novel perturbative method, proposed by Panda {\it et al.} [1] to solve the Helmholtz equation in two dimensions, is extended to three dimensions for general boundary surfaces. Although a few numerical works are available in the literature…
This chapter presents some numerical methods to solve problems in the fractional calculus of variations and fractional optimal control. Although there are plenty of methods available in the literature, we concentrate mainly on approximating…
One of the fundamental differences of compressible fluid flows from incompressible fluid flows is the involvement of thermodynamics. This difference should be manifested in the design of numerical methods and seems often be neglected in…
We establish a deep connection between the Prandtl equations linearised around a quadratic shear flow, confluent hypergeometric functions of the first kind, and the Schr\"odinger operator. Our first result concerns an ODE and a spectral…
In this paper, the propagation of the blast (shock) waves in non-ideal gas atmosphere in rotational medium is studied using a power series method in cylindrical geometry. The flow variables are assumed to be varying according to the power…
The flow in a shock tube is extremely complex with dynamic multi-scale structures of sharp fronts, flow separation, and vortices due to the interaction of the shock wave, the contact surface, and the boundary layer over the side wall of the…
Particle Image Velocimetry (PIV) and Particle Tracking Velocimetry (PTV) have been employed to investigate the dynamics of finite-size spherical particles, slightly heavier than the carrier fluid, in a horizontal turbulent square duct flow.…
Longstanding problems regarding the causality of the diffusion equation are resolved through a class of exact solutions. A universal differential solution for diffusive processes is derived that is causal and exact at any analytic point in…
When a plane shock hits a wedge head on, it experiences a reflection-diffraction process and then a self-similar reflected shock moves outward as the original shock moves forward in time. Experimental, computational, and asymptotic analysis…
The general analytical solution for the static spherically symmetric metric supported by a perfect fluid with isothermal (proportional) equation-of-state $p = w \rho$ is not known at the time of this writing, except for the trivial cases…
This paper presents two approaches to mathematical modelling of a synthetic seismic pulse, and a comparison between them. First, a new analytical model is developed in two-dimensional Cartesian coordinates. Combined with an initial…
Numerical solutions of the laminar Prandtl boundary-layer and Navier-Stokes equations are considered for the case of the two-dimensional uniform flow past an impulsively-started circular cylinder. We show how Prandtl's solution develops a…
We investigate the Cauchy problem for a fluid-particle interaction model in $\mathbb{R}^3$. This model consists of the compressible barotropic Navier-Stokes equations and the Vlasov-Fokker-Planck equation coupled together via the…
In this work, we analytically derive the exact closed dynamical equations for a liquid with short-ranged interactions in large spatial dimensions using the same statistical mechanics tools employed to analyze Brownian motion. Our derivation…
Non-perturbative exact flow equations describe the scale dependence of the effective average action. We present a numerical solution for an approximate form of the flow equation for the potential in a three-dimensional N-component scalar…
We prove the global existence of weak solutions to the Navier-Stokes equations of compressible heat-conducting fluids in two spatial dimensions with initial data and external forces which are large and spherically symmetric. The solutions…
Physics-informed neural networks (PINNs) are employed to solve the classical compressible flow problem in a converging-diverging nozzle. This problem represents a typical example described by the Euler equations, thorough understanding of…
In this work we study the dynamic behaviour of compound shells of revolution partially filled with an ideal incompressible fluid based on boundary-value problems. New analytical mathematical model with corresponding discrete scheme for the…
The general problem of shock formation in three space dimensions was solved by D. Christodoulou in his 2007 monograph: 'The Formation of Shocks in 3-dimensional Fluids'. In this work also a complete description of the maximal development of…