A hyperbolic Poisson solver for wall distance computation on irregular triangular grids

2021 ◽  
pp. 110599
Author(s):  
Hiroaki Nishikawa
Keyword(s):  
Distance Computation ◽  
Wall Distance ◽  
Triangular Grids ◽  
Poisson Solver

scholarly journals POS0239 ROOT JOINT INVOLVEMENT IN SPONDYLOARTHRITIS: A POST-HOC ANALYSIS FROM THE INTERNATIONAL ASAS-PERSPA STUDY

2021 ◽  
Vol 80 (Suppl 1) ◽  
pp. 340.1-341
Author(s):  
N. Ziade ◽  
J. El-Hajj ◽  
J. Rassi ◽  
S. Hlais ◽  
C. López-Medina ◽  
...  
Keyword(s):  
Psoriatic Arthritis ◽  
Positive Answer ◽  
Categorical Variables ◽  
Joint Involvement ◽  
Main Diagnosis ◽  
Post Hoc Analysis ◽  
Wall Distance ◽  
History Of ◽  
Axial Disease ◽  
Post Hoc

Background:In patients with spondyloarthritis (SpA), root joint diseases (RJD), i.e. hip or shoulder involvement, may be associated with a distinct disease phenotype compared to those with other affected joints. The ASAS-PerSpA study (PERipheral involvement in SPondyloArthritis) [1], offers a unique opportunity to study the phenotypes of patients with RJD in a global cohort.Objectives:Primary objective was to compare the clinical characteristics of SpA patients with and without RJD. Secondary objectives were to compare the prevalence of RJD across the different SpA subtypes and the different regions of the world, compare the severity of axial disease as well as the disease burden in SpA patients with and without RJD.Methods:This is a post-hoc analysis of the ASAS-PerSpA study, which included 4,465 patients with any subtype of SpA (axial SpA (axSpA), peripheral SpA (pSpA), psoriatic arthritis (PsA), inflammatory bowel disease associated SpA (IBD-SpA), reactive arthritis (ReA) and Juvenile SpA (Juv-SpA)) according to the rheumatologist’s diagnosis. RJD was defined as a positive answer by the investigator to the following question: “Do you consider that the patient has ever suffered from RJD (e.g. hip, shoulder) related to SpA?” In case of a positive answer, a potential specific treatment (e.g. Total Articular Replacement) was investigated. The patient’s characteristics were compared between those with and without RJD involvement, using Chi-2 or Fisher exact test for the categorical variables and t-test for the continuous variables. Two separate multivariable stepwise binary logistic regression analyses were conducted to identify factors associated with the dependent variables “hip involvement” and “shoulder involvement”.Results:RJD occurred in 1,503 patients (33.7%), with more prevalent hip (24.2%) than shoulder (13.2%) involvement. The prevalence of RJD as a group was the highest in Juv-SpA (52.7%), followed by pSpA (44.3%) and axSpA (33.9%). The highest prevalence of RJD was found in Asia and the lowest in Europe and North America. Among patients with hip involvement, 6.0% had a history of hip replacement (highest in the Middle East and North Africa and Latin America); among patients with shoulder involvement, 0.8% had a history of shoulder replacement. Hip had a distinct pattern of associations compared to shoulder involvement (Figure 1). Hip involvement was significantly associated with the SpA main diagnosis (highest in pSpA, lowest in PsA), younger age at first SpA symptom, lower prevalence of family history of psoriasis, positive HLA-B27, occiput-to-wall distance>0, and treatment with cs-DMARDs and b-DMARDs. Shoulder involvement was associated with the SpA main diagnosis (highest in Juv-SpA and pSpA, lowest in axSpA), older age at first SpA symptom, higher prevalence of enthesitis, dactylitis, tender joints count, IBD, occiput-to-wall distance>0, EQ5D score and treatment with cs-DMARDs.Conclusion:Hip involvement was more prevalent than shoulder involvement in patients with SpA, and had a distinct phenotype resembling axial disease whereas shoulder involvement was mostly associated with features of peripheral disease. Hip and shoulder involvement should be analyzed separately in future studies rather than under the RJD entity.References:[1]Lopez-medina, C. et al. Prevalence and Distribution of Peripheral Musculoskeletal Manifestations in Axial Spondyloarthritis, Peripheral Spondyloarthritis and Psoriatic Arthritis: Results of the International, Cross-sectional ASAS-PerSpA Study. RMD Open; 2021;7:e001450.Disclosure of Interests:None declared

A Domain-Decomposed Fast Poisson Solver on a Rectangle

1987 ◽  
Vol 8 (1) ◽  
pp. s14-s26 ◽  
Author(s):  
Tony F. Chan ◽  
Diana C. Resasco
Keyword(s):  
Poisson Solver ◽  
Fast Poisson Solver

A Note on Modeling of Nano-Scale Thermal Flow via the Lattice Boltzmann Method

2012 ◽  
Author(s):  
P. Lopez ◽  
Y. Bayazitoglu
Keyword(s):  
Distribution Function ◽  
Free Path ◽  
Knudsen Number ◽  
Reference Data ◽  
Mean Free Path ◽  
Knudsen Layer ◽  
High Order ◽  
Distance Functions ◽  
Transition Flow ◽  
Wall Distance

Lattice Boltzmann (LB) method models have been demonstrated to provide an accurate representation of the flow characteristics in rarefied flows. Conditions in such flows are characterized by the Knudsen number (Kn), defined as the ratio between the gas molecular Mean Free Path ( MFP, λ) and the device characteristic length (L). As the Knudsen number increases, the behavior of the flow near the walls is increasingly dominated by interactions between the gas molecules and the solid surface. Due to this, linear constitutive relations for shear stress and heat flux, which are assumed in the Navier-Stokes-Fourier (NSF) system of equations, are not valid within the Knudsen Layer (KL). Fig. 1 illustrates the characteristics of the velocity field within the Knudsen layer in a shear-driven flow. It is easily observed that although the NSF equations with slip flow boundary conditions (represented by dashed line) can predict the velocity profile in the bulk flow region, they fail to capture the flow characteristics inside the Knudsen layer. Slip flow boundary conditions have also been derived using the integral transform technique [1]. Various methods have been explored to extend the applicability of LB models to higher Knudsen number flows, including using higher order velocity sets, and using wall-distance functions to capture the effect of the walls on the mean free path by incorporating such functions on the determination of the local relaxation parameters. In this study, a high order velocity model which contains a two-dimensional, thirteen velocity direction set (e.g., D2Q13), as shown in Fig. 2, is used as the basis of the current LB model. The LB model consists of two independent distribution functions to simulate the density and temperature fields, while the Diffuse Scattering Boundary Condition (DSBC) method is used to simulate the fluid interaction with the walls. To further improve the characterization of transition flow conditions expected in nano-scale heat transfer, we explored the implementation of two wall-distance functions, derived recently based on an integrated form of a probability distribution function, to the high-order LB model. These functions are used to determine the effective mean free path values throughout the height of the micro/nano-channel, and the resulting effect is first normalized and then used to determine local relaxation times for both momentum and energy using a relationship based on the local Knudsen number. The two wall-distance functions are based on integral forms of 1) the classical probability distribution function, ψ(r) = λ0−1e−r/λ0, derived by Arlemark et al [2], in which λ0represents the reference gas mean free path, and 2) a Power-Law probability distribution function, derived by Dongari et al [3]. Thus, the probability that a molecule travels a distance between r and r+dr between two successive collisions is equal to ψ(r)dr. The general form of the integral of the two functions used can be described by ψ(r) = C − f(r), where f(r) represents the base function (exponential or Power Law), and C is set to 1 so that the probability that a molecule will travel a distance r+dr without a collision ranges from zero to 1. The performance of the present LB model coupled with the implementation of the two wall-distance functions is tested using two classical flow cases. The first case considered is that of isothermal, shear-driven Couette flow between two parallel, horizontal plates separated by a distance H, moving in opposite directions at a speed of U0. Fig. 3 shows the normalized velocity profiles across the micro-channel height for various Knudsen numbers in the transition flow regime based on our LB models as compared to data based on the Linearized Boltzmann equation [4]. The results show that our two LB models provide results that are in excellent agreement with the reference data up to the high end of the transition flow regime, with Knudsen numbers greater than 1. The second case is rarefied Fourier flow within horizontal, parallel plates, with the plates being stationary and set to a constant temperature (TTop > TBottom), and the Prandtl number is set to 0.67 to match the reference data based on the Direct Simulation Monte Carlo (DSMC) method [5]. Fig. 4 shows the normalized temperature profiles across the microchannel height for various Knudsen numbers in the slip/transition How regime. For the entire Knudsen number range studied, our two LB models provide temperature profiles that are in excellent agreement with the non-linear profile seen in the reference data. The results obtained show that the effective MFP relationship based on the exponential function improves the results obtained with the high order LB model for both shear-driven and Fourier flows up to Kn∼1. The results also show that the effective MFP relationship based on the Power Law distribution function greatly enhances the results obtained with the high order LB model for the two cases addressed, up to Kn∼3. In conclusion, the resulting LB models represent an effective tool in modeling non-equilibrium gas flows expected within micro/nano-scale devices.

Sign in / Sign up

Export Citation Format

Share Document