In this work we investigate the pricing of swing options in a model where the underlying asset follows a jump diffusion process. We focus on the derivation of the partial integro-differential equation (PIDE) which will be applied to swing contracts and construct a novel pay-off function from a tree-based pay-off matrix that can be used as initial condition in the PIDE formulation. For valuing swing type derivatives we develop a theta implicit-explicit finite difference scheme to discretize the PIDE using a Gaussian quadrature method for the integral part. Based on known results for the classical theta-method the existence and uniqueness of solution to the new implicit-explicit finite difference method is proven. Various numerical examples illustrate the usability of the proposed method and allow us to analyse the sensitivity of swing options with respect to model parameters. In particular the effects of number of exercise rights, jump intensities and dividend yields will be investigated in depth.

Based on the field velocity method, a novel approach for simulating unsteady pitching and plunging motion of an airfoil is presented in this paper. Responses to pitching and plunging motions of the airfoil are simulated under different conditions. The obtained results are compared with those of moving grid method and good agreement is achieved. In the conventional field velocity method, the Euler solver is usually used to simulate the movement of the airfoil. However, when viscous effect is considered, unsteady Navier-Stokes equations have to be solved and the viscous flux correction must be taken into account. In this work, the viscous flux correction is introduced into the conventional field velocity method when non-uniform grid speed distribution is occurred. Numerical experiments for the flow around NACA0012 airfoil showed that the proposed approach can well simulate viscous moving boundary flow problems.

A local domain-free discretization-immersed boundary method (DFD-IBM) is presented in this paper to solve incompressible Navier-Stokes equations in the primitive variable form. Like the conventional immersed boundary method (IBM), the local DFD-IBM solves the governing equations in the whole domain including exterior and interior of the immersed object. The effect of immersed boundary to the surrounding fluids is through the evaluation of velocity at interior and exterior dependent points. To be specific, the velocity at interior dependent points is computed by approximate forms of solution and the velocity at exterior dependent points is set to the wall velocity. As compared to the conventional IBM, the present approach accurately implements the non-slip boundary condition. As a result, there is no flow penetration, which is often appeared in the conventional IBM results. The present approach is validated by its application to simulate incompressible viscous flows around a circular cylinder. The obtained numerical results agree very well with the data in the literature.

Many engineering structures exhibit frequency dependent characteristics and analyses of these structures lead to frequency dependent eigenvalue problems. This paper presents a novel perturbative iteration (PI) algorithm which can be used to effectively and efficiently solve frequency dependent eigenvalue problems of general frequency dependent systems. Mathematical formulations of the proposed method are developed and based on these formulations, a computer algorithm is devised. Extensive numerical case examples are given to demonstrate the practicality of the proposed method. When all modes are included, the method is exact and when only a subset of modes are used, very accurate results are obtained.

This study presents a modification of the central-upwind Kurganov scheme for approximating the solution of the 2D Euler equation. The prototype, extended from a 1D model, reduces substantially less dissipation than expected. The problem arises from over-restriction of some slope limiters, which keep slopes between interfaces of cells to be Total-Variation-Diminishing. This study reports the defect and presents a re-derived optimal formula. Numerical experiments highlight the significance of this formula, especially in long-time, large-scale simulations.

This paper reports an improved constitutive model for the shear creep behavior of offwhite marbles which are selected from slope and underground cavern and contain green schist’s weak structural planes. The shear creep behavior of the samples is characterized using the rheological tests. Based on the experimental measurements on mechanical properties under different normal stress conditions, an improved model is proposed to analyze the experimental results. It is demonstrated from a further discussion that such model can reflect the non-linear creep characteristics of structural planes, and especially, it is suitable for description of the viscoelastic and viscoplastic deformation behavior of structural planes.

This work is concerned with the numerical simulations for two reaction-diffusion systems, i.e., the Brusselator model and the Gray-Scott model. The numerical algorithm is based upon a moving finite element method which helps to resolve large solution gradients. High quality meshes are obtained for both the spot replication and the moving wave along boundaries by using proper monitor functions. Unlike [33], this work finds out the importance of the boundary grid redistribution which is particularly important for a class of problems for the Brusselator model. Several ways for verifying the quality of the numerical solutions are also proposed, which may be of important use for comparisons.

Based on the theory of Lie group analysis, the full plastic torsion of rod with arbitrary shaped cross sections that consists in the equilibrium equation and the non-linear Saint Venant-Mises yield criterion is studied. Full symmetry group admitted by the equilibrium equation and the yield criterion is a finitely generated Lie group with ten parameters. Several subgroups of the full symmetry group are used to generate invariants and group invariant solutions. Moreover, physical explanations of each group invariant solution are discussed by all appropriate transformations. The methodology and solution techniques used belong to the analytical realm.