The Riemann Problem for a Blood Flow Model in Arteries

In this paper, the Riemann solutions of a reduced 6×6 blood flow model in medium-sized to large vessels are constructed. The model is non-strictly hyperbolic and non-conservative in nature, which brings two difficulties of the Riemann problem. One is the appearance of resonance while the other one is loss of uniqueness. The elementary waves include shock wave, rarefaction wave, contact discontinuity and stationary wave. The stationary wave is obtained by solving a steady equation. We construct the Riemann solutions especially when the steady equation has no solution for supersonic initial data. We also verify that the global entropy condition proposed by C.Dafermos can be used here to select the physical relevant solution. The Riemann solutions may contribute to the design of numerical schemes, which can apply to the complex blood flows.     

Field Model for Complex Ionic Fluids: Analytical Properties and Numerical Investigation

In this paper, we consider the field model for complex ionic fluids with anenergy variational structure, and analyze the well-posedness to this model with regularized kernels. Furthermore, we deduce the estimate of the maximal density function to quantify the finite size effect. On the numerical side, we adopt a finite volume scheme to the field model, which satisfies the following properties: positivity-preserving, mass conservation and energy dissipation. Besides, series of numerical experiments are provided to demonstrate the properties of the steady state and the finitesize effect by showing the equilibrium profiles with different values of the parameterin the kernel.     

Flow in Collapsible Tubes with Discontinuous Mechanical Properties: Mathematical Model and Exact Solutions

We formulate a one-dimensional time-dependent non-linear mathematical model for some types of physiological fluid flow in collapsible tubes with discontinuous material properties. The resulting 6×6 hyperbolic system is analysed and the associated Riemann problem is solved exactly. Although the solution algorithm deals with idealised cases, it is nonetheless uniquely well-suited for assessing the performance of numerical methods intended for simulating more general situations. Moreover, our model may be a useful starting point for numerical calculations of realistic flows involving rapid and discontinuous material property variations. One important example in mind is the simulation of blood flow in medium-to-large veins in humans. Finally, we also discuss some peculiarities of the model regarding the loss of strict hyperbolicity and uniqueness. In particular we show an example in which the solution of the Riemann problem is non unique.     

老年ED病人阴茎背动脉横切面积和血流量研究

目的 :探讨老年人血流动力学因素在勃起功能障碍 (ED)中的作用。　方法 :随机抽取 40例勃起功能正常和 5 9例老年ED病人 ,先以脉冲超声波多普勒探测阴茎背动脉横切面图形和平均流速时间积分 ,再用微机图像扫描仪自动测量图形面积 ,最后计算出阴茎背动脉每分血流量。　结果 :勃起功能正常不同年龄组间阴茎背动脉横切面积和血流量均无显著性差异 (P >0 0 5 ) ;勃起功能正常与ED相同年龄两组间阴茎背动脉横切面积有显著性差异 (P <0 0 5 ) ,血流量有非常显著性差异 (P <0 0 1)。　结论 :血管横切面积缩小及血流量降低在老年ED流行病学中起重要作用。     

Extrapolation Cascadic Multigrid Method for Cell-Centered FV Discretization of Diffusion Equations with Strongly Discontinuous and Anisotropic Coefficients

Extrapolation cascadic multigrid (EXCMG) method with conjugate gradientsmoother is very efficient for solving the elliptic boundary value problems with linearfinite element discretization. However, it is not trivial to generalize the vertex-centredEXCMG method to cell-centered finite volume (FV) methods for diffusion equationswith strongly discontinuous and anisotropic coefficients, since a non-nested hierarchyof grid nodes are used in the cell-centered discretization. For cell-centered FV schemes,the vertex values (auxiliary unknowns) need to be approximated by cell-centered ones(primary unknowns). One of the novelties is to propose a new gradient transfer (GT)method of interpolating vertex unknowns with cell-centered ones, which is easy to implement and applicable to general diffusion tensors. The main novelty of this paper isto design a multigrid prolongation operator based on the GT method and splitting extrapolation method, and then propose a cell-centered EXCMG method with BiCGStabsmoother for solving the large linear system resulting from linear FV discretizationof diffusion equations with strongly discontinuous and anisotropic coefficients. Numerical experiments are presented to demonstrate the high efficiency of the proposedmethod.     

A Generalized Numerical Approach for Modeling Multiphase Flow and Transport in Fractured Porous Media

A physically based numerical approach is presented for modeling multiphase flow and transport processes in fractured rock. In particular, a general framework model is discussed for dealing with fracture-matrix interactions, which is applicable to both continuum and discrete fracture conceptualization. The numerical modeling approach is based on a general multiple-continuum concept, suitable for modeling any types of fractured reservoirs, including double-, triple-, and other multiple-continuum conceptual models. In addition, a new, physically correct numerical scheme is discussed to calculate multiphase flow between fractures and the matrix, using continuity of capillary pressure at the fracture-matrix interface. The proposed general modeling methodology is verified in special cases using analytical solutions and laboratory experimental data, and demonstrated for its application in modeling flow through fractured vuggy reservoirs.     

心脏手术后混合静脉血氧饱和度与血容量心指数相关分析

为阐明混合静脉血氧饱和度（ＳｖＯ２）是否能有效监测术后血容量（ＢＶ）及心输出量（ＣＯ）变化。作者对２４例心脏术后病例分别于术毕处于机械通气及睡眠状态（术后Ｉ组），术后６小时处于机械通气及清醒状态（术后Ｉ组），及术后２４小时处于自主呼吸及清醒状态（术后ＩＩ组）下测定ＳｖＯ２与ＢＶ、心指数（ＣＩ）进行相关分析。结果：术后Ｉ组ＳｖＯ２与ＢＶ、ＣＩ相关系数分别为０．７８５６和０．８０４０（Ｐ＜０．００１）；术后ＩＩ组为０７７８１和０８８１５（Ｐ＜０００１）；术后ＩＩ组为０．７２４３和０．８５３３（Ｐ＜０．００１）。结论：心脏术后不同条件下ＳｖＯ２与ＢＶ、ＣＩ具显著相关性，ＳｖＯ２作为术后ＢＶ及ＣＯ变化的一种监测指标是敏感可靠的。     

Permanent Charge Effects on Ionic Flow: A Numerical Study of Flux Ratios and Their Bifurcation

Ionic flow carries electrical signals for cells to communicate with each other.The permanent charge of an ion channel is a crucial protein structure for flow properties while boundary conditions play a role of the driving force. Their effects on flowproperties have been analyzed via a quasi-one-dimensional Poisson-Nernst-Planckmodel for small and relatively large permanent charges. The analytical studies haveled to the introduction of flux ratios that reflect permanent charge effects and have auniversal property. The studies also show that the flux ratios have different behaviorsfor small and large permanent charges. However, the existing analytical techniquescan reveal neither behaviors of flux ratios nor transitions between small and large permanent charges. In this work we present a numerical investigation on flux ratios tobridge between small and large permanent charges. Numerical results verify the analytical predictions for the two extremal regions. More significantly, emergence of non-trivial behaviors is detected as the permanent charge varies from small to large. Inparticular, saddle-node bifurcations of flux ratios are revealed, showing rich phenomena of permanent charge effects by the power of combining analytical and numericaltechniques. An adaptive moving mesh finite element method is used in the numericalstudies.     

Asymptotic Structure of Cosmological Burgers Flows in One and Two Space Dimensions: A Numerical Study

We study the cosmological Burgers model, as we call it, which is a nonlinearhyperbolic balance law (in one and two spatial variables) posed on an expanding orcontracting background. We design a finite volume scheme that is fourth-order intime and second-order in space, and allows us to compute weak solutions containingshock waves. Our main contribution is the study of the asymptotic structure of thesolutions as the time variable approaches infinity (in the expanding case) or zero (inthe contracting case). We discover that a saddle competition is taking place whichinvolves, on one hand, the geometrical effects of expanding or contracting nature and,on the other hand, the nonlinear interactions between shock waves.     

Linear Stability Analysis and Gas Kinetic Scheme (GKS) Simulations of Instabilities in Compressible Plane Poiseuille Flow

The fundamental nature of flow instability in wall bounded flows changeswith Mach number. The objectives of this study are two-fold, (i) compute the instability modes in high Mach number Poiseuille flows using linear stability analysis (LSA)and, (ii) perform direct numerical simulations (DNS) of the instability developmentusing a solver based on gas kinetic method (GKM) for the purpose of code validationby comparison against LSA results. The LSA and DNS are performed for the case ofPoiseuille flow over a range of Mach numbers – from moderately supersonic to hypersonic speeds. First, LSA is employed to identify the most unstable mode over the rangeof Mach numbers. We then perform two sets of GKM-DNS to corroborate the LSA results over the Mach number range. In the first set of simulations, the background fieldis initially perturbed with the most unstable mode identified by LSA and the evolutionis monitored. It is shown that GKM-DNS accurately captures the exponential growthin kinetic energy for all Mach numbers. The second set of GKM-DNS simulations isperformed by superposing the background pressure field with random initial perturbations. After an initial transient period, the modes predicted by LSA dominate theDNS flow field evolution. The wave-vector and mode shapes of the dominant instability are well replicated by GKM-DNS at each Mach number. These insights in thelinear regime of high speed Poiseuille flow and validation of GKM are important forunderstanding and simulating wall bounded flows.     

An Edge-Based Smoothed Finite Element Method with TBC for the Elastic Wave Scattering by an Obstacle

Elastic wave scattering has received ever-increasing attention in military and medical fields due to its high-precision solution. In this paper, an edge-based smoothed finite element method (ES-FEM) combined with the transparent boundary condition (TBC) is proposed to solve the elastic wave scattering problem by a rigid obstacle with smooth surface, which is embedded in an isotropic and homogeneous elastic medium in two dimensions. The elastic wave scattering problem satisfies Helmholtz equations with coupled boundary conditions obtained by Helmholtz decomposition. Firstly, the TBC of the elastic wave scattering is constructed by using the analytical solution to Helmholtz equations, which can truncate the boundary value problem (BVP) in an unbounded domain into the BVP in a bounded domain. Then the formulations of ES-FEM with the TBC are derived for Helmholtz equations with coupled boundary conditions. Finally, several numerical examples illustrate that the proposed ES-FEM with the TBC (ES-FEM-TBC) can work effectively and obtain more stable and accurate solution than the standard FEM with the TBC (FEM-TBC) for the elastic wave scattering problem.     

Three Discontinuous Galerkin Methods for One- and Two-Dimensional Nonlinear Dirac Equations with a Scalar Self-Interaction

This paper develops three high-order accurate discontinuous Galerkin (DG) methods for the one-dimensional (1D) and two-dimensional (2D) nonlinear Dirac (NLD) equations with a general scalar self-interaction. They are the Runge-Kutta DG (RKDG) method and the DG methods with the one-stage fourth-order Lax-Wendroff type time discretization (LWDG) and the two-stage fourth-order accurate time discretization (TSDG). The RKDG method uses the spatial DG approximation to discretize the NLD equations and then utilize the explicit multistage high-order Runge-Kutta time discretization for the first-order time derivatives, while the LWDG and TSDG methods, on the contrary, first give the one-stage fourth-order Lax-Wendroff type and the two-stage fourth-order time discretizations of the NLD equations, respectively, and then discretize the first- and higher-order spatial derivatives by using the spatial DG approximation. The $L^2$ stability of the 2D semi-discrete DG approximation is proved in the RKDG methods for a general triangulation, and the computational complexities of three 1D DG methods are estimated. Numerical experiments are conducted to validate the accuracy and the conservation properties of the proposed methods. The interactions of the solitary waves, the standing and travelling waves are investigated numerically and the 2D breathing pattern is observed.     

Localized Exponential Time Differencing Method for Shallow Water Equations: Algorithms and Numerical Study

In this paper, we investigate the performance of the exponential time differencing (ETD) method applied to the rotating shallow water equations. Comparingwith explicit time stepping of the same order accuracy in time, the ETD algorithmscould reduce the computational time in many cases by allowing the use of large timestep sizes while still maintaining numerical stability. To accelerate the ETD simulations, we propose a localized approach that synthesizes the ETD method and overlapping domain decomposition. By dividing the original problem into many subdomainproblems of smaller sizes and solving them locally, the proposed approach could speedup the calculation of matrix exponential vector products. Several standard test casesfor shallow water equations of one or multiple layers are considered. The results showgreat potential of the localized ETD method for high-performance computing becauseeach subdomain problem can be naturally solved in parallel at every time step.     

Hemodynamics and Oxygen Transport after Partial and Total Blood Exchange with Pyridoxalated Polyhemoglobin in Dogs

The effects of a pyridoxalated polyhemoglobin solution (SFH-PLP)n-solution) on cardiovascular hemodynamics and oxygen transport were investigated in a model of partial and total blood exchange in seven dogs. Cardiac output, mean arterial pressure and heart rate were essentially unchanged, even after total blood exchange, due to the long plasma half-disappearance time of (SFH-PLP)n (36 h) and due to the addition of albumin to the solution. The oxygen-binding capacity of (SFH-PLP)n was 1.1 to 1.2 ml O2/g hb. Oxygen availability was reduced to about 50%, resulting from the low hemoglobin concentration and the decreased oxygen-binding capacity of (SFH-PLP)n. Since cardiac output did not increase, O2-consumption was maintained by an increase in O2-extraction from 21 to about 50%. However the decrease in mixed venous PO2 to values not below 30 mmHg (4.00 kPa) proves the sufficient unloading capacity of (SFH-PLP)n. The adequate tissue oxygenation of (SFH-PLP)n could be demonstrated by the lack of a metabolic acidosis, the essentially unchanged PO2-histograms of the skeletal muscle and the only moderate decrease in mixed venous PO2. Four dogs survived for more than 3 days; three of them were long-term survivors. This suggests that oxygen supply was maintained by (SFH-PLP)n until red blood cells were restored.     

Development of Design Methods of a Centrifugal Blood Pump with In Vitro Tests, Flow Visualization, and Computational Fluid Dynamics: Results inHemolysis Tests

Abstract There are few established engineering guidelines aimed at reducing hemolysis for the design of centrifugal blood pumps. In this study, a fluid dynamic approach was applied to investigate hemolysis in centrifugal pumps. Three different strategies were integrated to examine the relationship between hemolysis and flow patterns. Hemolytic performances were evaluated in in vitro tests and compared with the flow patterns analyzed by flow visualization and computational fluid dynamic (CFD). Then our group tried to establish engineering guidelines to reduce hemolysis in the development of centrifugal blood pumps. The commercially available Nikkiso centrifugal blood pump (HPM-15) was used as a standard, and the dimensions of 2 types of gaps between the impeller and the casing, the axial and the radial gap, were varied. Four impellers with different vane outlet angles were also prepared and tested. Representative results of the hemolysis tests were as follows: The axial gaps of 0.5, 1.0, and 1.5 mm resulted in normalized index of hemolysis (NIH) values of 0.0028, 0.0013 and 0.0008 g/100 L, respectively. The radial gaps of 0.5 and 1.5 mm resulted in NIH values of 0.0012 and 0.0008 g/100 L, respectively. The backward type vane and the standard one resulted in NIH values of 0.0013 and 0.0002 g/100 L, respectively. These results revealed that small gaps led to more hemolysis and that the backward type vane caused more hemolysis. Therefore, the design parameters of centrifugal blood pumps could affect their hemolytic performances. In flow visualization tests, vortices around the impeller outer tip and tongue region were observed, and their patterns varied with the dimensions of the gaps. CFD analysis also predicted high shear stress consistent with the results of the hemolysis tests. Further investigation of the regional flow patterns is needed to discuss the cause of the hemolysis in centrifugal blood pumps.     

Numerical Stability Analysis for a Stationary and Translating Droplet at Extremely Low Viscosity Values Using the Lattice Boltzmann Method Color-Gradient Multi-Component Model with Central Moments Formulation

Multicomponent models based on the Lattice Boltzmann Method (LBM) have clear advantages with respect to other approaches, such as good parallel performances and scalability and the automatic resolution of breakup and coalescence events. Multicomponent flow simulations are useful for a wide range of applications, yet many multicomponent models for LBM are limited in their numerical stability and therefore do not allow exploration of physically relevant low viscosity regimes. Here we perform a quantitative study and validations, varying parameters such as viscosity, droplet radius, domain size and acceleration for stationary and translating droplet simulations for the color-gradient method with central moments (CG-CM) formulation, as this method promises increased numerical stability with respect to the non-CM formulation. We focus on numerical stability and on the effect of decreasing grid-spacing, i.e. increasing resolution, in the extremely low viscosity regime for stationary droplet simulations. The effects of small- and large-scale anisotropy, due to grid-spacing and domain-size, respectively, are investigated for a stationary droplet. The effects on numerical stability of applying a uniform acceleration in one direction on the domain, i.e. on both the droplet and the ambient, is explored into the low viscosity regime, to probe the numerical stability of the method under dynamical conditions.