Laboratory Simulations of Supernova Shockwave Propagation

Supernovae launch spherical shocks into the circumstellar medium (CSM). These shocks have high Mach numbers and may be radiative. We have created similar shocks in the laboratory by focusing laser pulses onto the tip of a solid pin surrounded by ambient gas; ablated material from the pin rapidly expands and launches a shock through the surrounding gas. Laser pulses were typically 5 ns in duration with ablative energies ranging from 1–150 J. Shocks in ambient gas pressures of ~1 kPa were observed at spatial scales of up to 5 cm using optical cameras with schlieren. Emission spectroscopy data were obtained to infer electron temperatures (< 10 eV). In this experiment we have observed a new phenomena; at the edge of the radiatively heated gas ahead of the shock, a second shock forms. The two expanding shocks are simultaneously visible for a time, until the original shock stalls from running into the heated gas. The second shock remains visible and continues to expand. A minimum condition for the formation of the second shock is that the original shock is super-critical, i.e., the temperature distribution ahead of the original shock has an inflexion point. In a non-radiative control experiment the second shock does not form. We hypothesize that a second shock could form in the astrophysical case, possibly in radiative supernova remnants such as SN1993J, or in shock-CSM interaction.     

结构动力响应计算结果对应于不同阻尼的修正方法

本文提出了一种当结构系统采用Rayleigh阻尼且阻尼参数发生变化时，对系统动力反应结果直接进行修正的方法并通过算例对其精度进行了验证。这一方法可以提高大型工程结构动力计算的效率。     

Calculation of strongly singular and hypersingular surface integrals

Efficient numerical computation of integrals defined on closed surfaces in ℝ³ with non-integrable point singularities that arise in physical geodesy is discussed. The method is based on the use of polar coordinates and the definition of integrals with non-integrable point singularities as Hadamard finite part integrals. First the behavior of singular integrals under smooth parameter transformations is studied, and then it is shown how they can be reduced to absolutely integrable functions over domains in ℝ². The correction terms that usually arise if the substitution rule is formally applied, in contrast to absolutely integrable functions, are calculated. It is shown how to compute the regularized integrals efficiently, and, numerical efforts for various orders of singularity are compared. Finally, efficient numerical integration methods are discussed for integrals of functions that are defined as singular integrals, a task that typically arises in Galerkin boundary element methods. Received: 15 April 1997 / Accepted: 7 May 1998     

Certified solutions for hydraulic structures using the node‐based smoothed point interpolation method (NS‐PIM)

A meshfree node‐based smoothed point interpolation method (NS‐PIM), which has been recently developed for solid mechanics problems, is applied to obtain certified solutions with bounds for hydraulic structure designs. In this approach, shape functions for displacements are constructed using the point interpolation method (PIM), and the shape functions possess the Kronecker delta property and permit the straightforward enforcement of essential boundary conditions. The generalized smoothed Galerkin weak form is then applied to construct discretized system equations using the node‐based smoothed strains. As a very novel and important property, the approach can obtain the upper bound solution in energy norm for hydraulic structures. A 2D gravity dam problem and a 3D arch dam problem are solved, respectively, using the NS‐PIM and the simulation results of NS‐PIM are found to be the upper bounds. Together with standard fully compatible FEM results as a lower bound, we have successfully determined the solution bounds to certify the accuracy of numerical solutions. This confirms that the NS‐PIM is very useful for producing certified solutions for the analysis of huge hydraulic structures. Copyright © 2009 John Wiley & Sons, Ltd.     

Dynamics of evapotranspiration from a riparian pond complex in the Western Boreal Forest,Alberta, Canada

The relative contributions to total actual evapotranspiration (AET) from pond and riparian areas in a pond‐wetland complex in the Western Boreal Plain (WBP) of northern Alberta are measured using the Bowen ratio energy balance technique. Measurements show that a pond typical of the WBP evaporates at a rate more than twice that of the adjacent riparian peatland. Relating the actual to potential evapotranspiration over both surfaces yields Priestley–Taylor α coefficients of 0·69 and 1·11 for the peatland and pond respectively. Further results demonstrate that the sheltering and turbulent influences of the adjacent forested areas must be considered in the processes governing the permanence of WBP ponds. That is, forestry practices may inadvertently enhance the evaporative losses from the ponds, over and above the controls exerted by the regional climate. Copyright © 2006 John Wiley & Sons, Ltd.     

水平集和无网格耦合法在裂纹扩展中的应用

提出了一种模拟裂纹扩展的水平集和无网格耦合方法。由于水平集和无网格方法都是建立在离散节点上,因而可以很自然地实现耦合。在该方法中,两个在裂尖处相互正交的水平集不仅用于描述裂纹的几何形态和裂尖位置,而且用于建立无网格伽辽金法（简称EFGM）不连续近似函数中的Heaviside跳跃项和裂尖处的Westergaard扩展项。当裂纹扩展时,则由水平集更新算法确定新裂纹的位置。水平集和无网格耦合法无需使用可视法、衍射法或透明法,克服了这些方法在裂尖处人为引入的不连续且能很好地再生 奇异场;而且节点影响域不受裂纹线切割的影响,在计算中往往使用较小的影响域,保持了整体刚度矩阵的带状、稀疏性;另外,水平集简化了扩展节点的选取和附加函数的建立,其更新过程无需求解演化方程,实现简单且易于编程。数值算例表明本文方法具有较高的计算精度,其模拟的裂纹扩展路径与试验结果吻合得很好,从而验证了本文方法的正确性和可行性。     

稠油油藏热-流体-力学耦合模型研究及应用

在稠油油藏开发中,由于原油黏度高一般采用注蒸汽开采。基于连续介质力学理论,考虑了热对流的影响,建立了蒸汽注入条件下对地层压力、变形和有效应力定量评价的改进的热-流体-力学耦合数学模型;应用全隐式顺序Galerkin有限元数值解方案对注蒸汽井热-流体-力学耦合过程进行了数值模拟。计算结果表明,由于地层流体高温膨胀引起的高压力,会导致位移、变形,甚至地层结构破裂;温度对地层破裂形态的影响显著。研究表明,这个改进模型比传统模型更加准确、实用,可以用于蒸汽注入速率优化和油藏、地质、热-流动力反应、地应力水平等综合作用效应研究。     

基于峰值频率的薄层厚度计算公式及其近似(英文)

调谐厚度范围内薄层厚度定量预测一直是地震勘探面临的挑战之一,目前多数讨论仅限于顶底反射系数等幅反极性的薄层,对于其他薄层类型尚无系统研究.本文将所有薄层划分为四类:等幅反极性薄层、不等幅反极性薄层、等幅同极性薄层、不等幅同极性型薄层;通过理论推导得到薄层地震峰值频率与厚度关系的一般表达式,针对该式为一个复杂非线性隐式、难于直接应用求取薄层厚度的难题,采用三角函数的泰勒展开式进行简化,给出每类薄层厚度定量估算的近似公式,并系统讨论了各阶近似公式的精度.与传统的利用振幅信息求取薄层厚度的方法相比,本文方法的精度更高,且不受顶底反射系数绝对大小的影响,便于实际应用.     

Deconvolution with wavelets and vaguelettes

The use of wavelets for the solution of convolution equations is studied as a possible alternative to the well-established Fast Fourier Transform (FFT) technique. Two possible solution strategies are investigated: (1) The use of wavelets for the representation of both the given data and the unknown solution. This leads to an algorithm with good de-noising and data-compression properties. In terms of computational efficiency this algorithm is inferior to FFT. (2) The use of wavelets for the representation of the unknown solution and of so-called vaguelettes for the representations of the given data. This leads to an algorithm which is even faster than FFT. Received: 14 October 1998 / Accepted: 30 November 1999     

Discontinuous Galerkin methods for advective transport in single-continuum models of fractured media

Accurate simulation of flow and transport processes in fractured rocks requires that flow in fractures and shear zones to be coupled with flow in the porous rock matrix. To this end, we will herein consider a single-continuum approach in which both fractures and the porous rock are represented as volumetric objects, i.e., as cells in an unstructured triangular grid with a permeability and a porosity value associated with each cell. Hence, from a numerical point of view, there is no distinction between flow in the fractures and the rock matrix. This enables modelling of realistic cases with very complex structures. To compute single-phase advective transport in such a model, we propose to use a family of higher-order discontinuous Galerkin methods. Single-phase transport equations are hyperbolic and have an inherent causality in the sense that information propagates along streamlines. This causality is preserved in our discontinuous Galerkin discretization. We can therefore use a simple topological sort of the graph of discrete fluxes to reorder the degrees-of-freedom such that the discretized linear system gets a lower block-triangular form, from which the solution can be computed very efficiently using a single-pass forward block substitution. The accuracy and utility of the resulting transport solver is illustrated through several numerical experiments.