اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدمحدودات الإنحدار الغير المتوازن في طرق البولتزمان الشبكية
Nonequilibrium entropy limiters in lattice Boltzmann methods
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نحن نبني نظاما من محدودي الإنزيم غير التعادل لطرق البولتزمان الشبكية (LBM). هذه المحدودين تمسح الاهتزازات غير الصحيحة بدون تباين الصدمات، ولا تؤثر على الحلول الناعمة. عموما، يقومون بنفس العمل لLBM مثل المحدودين الجريان لطرق الاختلافات المحدودة، والحجوم المحدودة وطرق العناصر المحدودة، ولكن لLBM فكرة أساسية وراء بناء برامج محدودي الإنزيم غير التعادل هي تحويل مجال لكمية مفردة - الإنزيم غير التعادل. هناك مجموعتان من المحدودين: (i) المستندة إلى تقييد الإنزيم غير التعادل (قص الإنزيم) و(ii) المستندة إلى تصفية الإنزيم غير التعادل (تصفية الإنزيم). وتوفر الخصائص الفيزيائية لLBM بعض الفوائد الإضافية: السيطرة على إنتاج الإنزيم وتقدير دقيق للتصحيح الصناعي المدخل. وتم اختبار المحدودين المبنيين على الأمثلة الرياضية التقليدية: أنبوبات الصدمة غير الحرارية بمعدل الكثافة الأولي 1:2 والحجرة المضغوطة المدحلة بشكل ثنائي الأبعاد لأرقام المكثفة Re بين 2000 و 7500 على شبكة كثيفة 100 * 100. وتنطبق جميع بناء المحدودين على التوازنات الكافية وغير الكافية.
We construct a system of nonequilibrium entropy limiters for the lattice Boltzmann methods (LBM). These limiters erase spurious oscillations without blurring of shocks, and do not affect smooth solutions. In general, they do the same work for LBM as flux limiters do for finite differences, finite volumes and finite elements methods, but for LBM the main idea behind the construction of nonequilibrium entropy limiter schemes is to transform a field of a scalar quantity - nonequilibrium entropy. There are two families of limiters: (i) based on restriction of nonequilibrium entropy (entropy trimming) and (ii) based on filtering of nonequilibrium entropy (entropy filtering). The physical properties of LBM provide some additional benefits: the control of entropy production and accurate estimate of introduced artificial dissipation are possible. The constructed limiters are tested on classical numerical examples: 1D athermal shock tubes with an initial density ratio 1:2 and the 2D lid-driven cavity for Reynolds numbers Re between 2000 and 7500 on a coarse 100*100 grid. All limiter constructions are applicable for both entropic and non-entropic quasiequilibria.
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