In this paper, we study carbon emission trading whose market is gaining in popularity as a policy instrument for global climate change. The mathematical model is presented for pricing options on CO2 emission allowance futures with jump diffusion processes, and a so-called fitted finite volume method is proposed to solve the pricing model for the spatial discretization, in which the Crank-Nicolson is employed for time stepping. In addition, the stability and the convergence of the fully discrete scheme are given, and some numerical results, which are compared with the closed form solution and the Monte Carlo simulation solution, are provided to demonstrate the rates of convergence and the robustness of the numerical method.

Jet impingement induced heat transfer is an important issue in engineering science. This paper presents results of large eddy simulation (LES) of normally impinging elliptic air-jet heat transfer at a Reynolds number of 4400, with orifice-to-plate distance fixed to be 5 in the unit of jet nozzle effective diameter . The elliptic aspect ratio (a/b) is 3/2. While the target wall is heated under some condition of constant heat flux. The LES are carried out using dynamic subgrid model and Open-FOAM. The distributions ofmean velocity components, velocity fluctuations, and subgrid stresses in vertical and radial directions, and the Nusselt numbers involving heat transfer through the target wall are discussed. The comparison with existing experimental and numerical results shows good agreement.

Von Neumann stability theory is applied to analyze the stability of a fully coupled implicit (FCI) scheme based on the lower-upper symmetric Gauss-Seidel (LU-SGS) method for inviscid chemical non-equilibrium flows. The FCI scheme shows excellent stability except the case of the flows involving strong recombination reactions, and can weaken or even eliminate the instability resulting from the stiffness problem, which occurs in the subsonic high-temperature region of the hypersonic flow field. In addition, when the full Jacobian of chemical source term is diagonalized, the stability of the FCI scheme relies heavily on the flow conditions. Especially in the case of high temperature and subsonic state, the CFL number satisfying the stability is very small. Moreover, we also consider the effect of the space step, and demonstrate that the stability of the FCI scheme with the diagonalized Jacobian can be improved by reducing the space step. Therefore, we propose an improved method on the grid distribution according to the flow conditions. Numerical tests validate sufficiently the foregoing analyses. Based on the improved grid, the CFL number can be quickly ramped up to large values for convergence acceleration.