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Direkte Numerische Simulation Пряме чисельне моделювання 直接数値シミュレーション Direkt numerisk simulering Direct numerical simulation Прямое численное моделирование Direct numerical simulation Simulation numérique directe

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Una simulazione numerica diretta (DNS) è un tecnica di simulazione numerica usata in fluidodinamica computazionale (CFD, Computational Fluid Dynamics). Può essere vista come la tecnica più fondamentale (e meno approssimata) della CFD, in quanto le equazioni di Navier-Stokes sono risolte numericamente senza l'utilizzo di alcun modello approssimato di turbolenza che vada ad effettuare una limitazione delle scale spaziali e temporali su cui effettuare l'integrazione. Quindi, di conseguenza, in una DNS è necessario integrare l'intera gamma di scale spaziali e temporali per riuscire a descrivere i fenomeni turbolenti. Tutte le scale spaziali della turbolenza devono essere risolte nella griglia computazionale, dalle più piccole scale dissipative, chiamate microscale di Kolmogorov, fino alla scal 直接数値シミュレーション（ちょくせつすうちシミュレーション、英: Direct Numerical Simulation、DNS）とは、流れ（層流や乱流）を数値的に解析するCFD手法の1つであり、以下の基礎方程式をそのまま（モデル化なしで）解き、流れに含まれる全ての大きさの渦をシミュレートすることである。 * 連続式（質量保存則） * 運動方程式（運動量保存則） ここでp は圧力、ρは密度、νは粘性係数、λはである。各項はそれぞれ、 * 左辺 - 第1項 : 時間項、第2項 : 移流項、第3項 : 圧力項、第4, 5項 : 粘性項 * 右辺 - 第1項 : 外力項 である。 Прямое численное моделирование (англ. DNS (Direct Numerical Simulation)) — один из методов численного моделирования течений жидкости или газа. Метод основан на численном решении системы уравнений Навье-Стокса и позволяет моделировать в общем случае движение вязких сжимаемых газов с учётом химических реакций, притом как для ламинарных, так и, несмотря на многочисленные споры, турбулентных случаев. Unter Direkter Numerischer Simulation, kurz DNS, versteht man eine Berechnungsmethode der Strömungsmechanik zur rechnerischen Lösung der vollständigen instationären Navier-Stokes-Gleichungen. Sie unterscheidet sich von anderen Berechnungsmethoden der Strömungsmechanik dadurch, dass kleinskalige turbulente Schwankungen numerisch in Raum und Zeit aufgelöst und nicht durch Turbulenzmodelle dargestellt werden. En analys med metoden Direkt Numerisk Simulering (Direct numerical simulation, DNS) är en simulering med CFD-teknik där Navier–Stokes ekvationer löses numeriskt utan att använda någon turbulensmodell. A direct numerical simulation (DNS) is a simulation in computational fluid dynamics (CFD) in which the Navier–Stokes equations are numerically solved without any turbulence model. This means that the whole range of spatial and temporal scales of the turbulence must be resolved. All the spatial scales of the turbulence must be resolved in the computational mesh, from the smallest dissipative scales (Kolmogorov microscales), up to the integral scale , associated with the motions containing most of the kinetic energy. The Kolmogorov scale, , is given by Since Пряме́ чи́сельне моделюва́ння (англ. DNS (Direct Numerical Simulation)) — один з методів чисельного моделювання течії рідини або газу. Метод ґрунтується на чисельному розв'язуванні системи рівнянь Нав'є — Стокса і дозволяє моделювати в загальному випадку рух в'язких стисливих газів з урахуванням хімічних реакцій, причому як для ламінарних, так і, попри численні суперечки, турбулентних випадків.

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Пряме́ чи́сельне моделюва́ння (англ. DNS (Direct Numerical Simulation)) — один з методів чисельного моделювання течії рідини або газу. Метод ґрунтується на чисельному розв'язуванні системи рівнянь Нав'є — Стокса і дозволяє моделювати в загальному випадку рух в'язких стисливих газів з урахуванням хімічних реакцій, причому як для ламінарних, так і, попри численні суперечки, турбулентних випадків. Однак DNS складно застосовне для розв'язування реальних задач, і частіше використовується в наукових розрахунках. Основна тому причина — високі вимоги до обчислювальних ресурсів. У прикладних задачах використовують переважно такі методи, як , DES і методи, засновані на розв'язуванні RANS-систем. Прямое численное моделирование (англ. DNS (Direct Numerical Simulation)) — один из методов численного моделирования течений жидкости или газа. Метод основан на численном решении системы уравнений Навье-Стокса и позволяет моделировать в общем случае движение вязких сжимаемых газов с учётом химических реакций, притом как для ламинарных, так и, несмотря на многочисленные споры, турбулентных случаев. Однако DNS сложно применим для решения реальных задач, и чаще используется в научных расчетах. Основная тому причина — высокие требования к вычислительным ресурсам. В прикладных задачах используют в основном такие методы, как LES, DES и методы, основанные на решении RANS-систем. 直接数値シミュレーション（ちょくせつすうちシミュレーション、英: Direct Numerical Simulation、DNS）とは、流れ（層流や乱流）を数値的に解析するCFD手法の1つであり、以下の基礎方程式をそのまま（モデル化なしで）解き、流れに含まれる全ての大きさの渦をシミュレートすることである。 * 連続式（質量保存則） * 運動方程式（運動量保存則） ここでp は圧力、ρは密度、νは粘性係数、λはである。各項はそれぞれ、 * 左辺 - 第1項 : 時間項、第2項 : 移流項、第3項 : 圧力項、第4, 5項 : 粘性項 * 右辺 - 第1項 : 外力項 である。 Una simulazione numerica diretta (DNS) è un tecnica di simulazione numerica usata in fluidodinamica computazionale (CFD, Computational Fluid Dynamics). Può essere vista come la tecnica più fondamentale (e meno approssimata) della CFD, in quanto le equazioni di Navier-Stokes sono risolte numericamente senza l'utilizzo di alcun modello approssimato di turbolenza che vada ad effettuare una limitazione delle scale spaziali e temporali su cui effettuare l'integrazione. Quindi, di conseguenza, in una DNS è necessario integrare l'intera gamma di scale spaziali e temporali per riuscire a descrivere i fenomeni turbolenti. Tutte le scale spaziali della turbolenza devono essere risolte nella griglia computazionale, dalle più piccole scale dissipative, chiamate microscale di Kolmogorov, fino alla scala integrale , associato alle componenti del moto del fluido che contengono la maggior componente dell'energia cinetica. La scala di Kolmogorov, , è dato da dove è la viscosità cinematica e è il tasso di dissipazione dell'energia cinetica. D'altra parte, la scala integrale dipende solitamente dalla scala spaziale determinata dalle condizioni al contorno. Per soddisfare questi requisiti di risoluzione, il numero di punti lungo una determinata direzione del reticolo di discretizzazione avente passo , deve essere in modo che la scala integrale sia contenuta all'interno del dominio computazionale e sia verificato anche la condizione in modo che la scala di Kolmogorov sia risolta. Poiché si ha che dove è il valore efficace (root mean square, RMS) della velocità, le relazioni precedenti implicano che un DNS tridimensionale richiede un numero di punti griglia , soddisfacente dove è il numero di Reynolds in regime turbolento: Quindi, la richiesta di risorse di calcolo in termini di memoria in un modello DNS cresce rapidamente con il numero di Reynolds (in particolare, come si dimostrerà, ). Inoltre, data l'enorme richiesta computazionale, l'integrazione della soluzione nel tempo deve essere effettuata con un metodo esplicito e non con uno implicito. Ciò significa che, per essere precisi, l'integrazione, per la maggior parte dei metodi di discretizzazione, deve essere effettuata con un passo temporale, , abbastanza piccolo da consentire a una particella fluida di spostare solo una frazione della spaziatura del reticolo in ogni iterazione. Questo è, ( è qui il numero di Courant). L'intervallo di tempo totale simulato è generalmente proporzionale alla scala del tempo di turbolenza dato da Combinando queste relazioni, e il fatto che deve essere dell'ordine di , il numero di passaggi di integrazione temporale deve essere proporzionale a . D'altra parte, dalle definizioni di , e dato sopra, ne segue e di conseguenza, il numero di passi temporali cresce anche come una legge di potenza del numero di Reynolds. Si può stimare che il numero di operazioni in virgola mobile richieste per completare la simulazione è proporzionale al numero di punti griglia e al numero di passi temporali e, in conclusione, il numero di operazioni aumenta man mano che , come accennato in precedenza. Pertanto, il costo computazionale di una DNS è molto elevato, anche a bassi numeri di Reynolds. Per i numeri di Reynolds riscontrati nella maggior parte delle applicazioni industriali, le risorse di calcolo richieste da una DNS supererebbero la capacità dei computer più potenti attualmente disponibili . Tuttavia, la simulazione numerica diretta è uno strumento utile nella ricerca fondamentale nella turbolenza. Utilizzando il DNS è possibile eseguire "esperimenti numerici" ed estrarre da essi informazioni difficili o impossibili da ottenere in laboratorio, consentendo una migliore comprensione della fisica della turbolenza. Inoltre, le simulazioni DNS sono utili nello sviluppo di modelli di turbolenza per applicazioni pratiche, quali i modelli in scala di sottoreti per la formulazione LES e modelli per metodi che risolvono le equazioni di Navier-Stokes mediati da Reynolds (RANS). Questo viene fatto mediante test "a priori", in cui i dati di input per il modello sono presi da una simulazione DNS, oppure mediante test "a posteriori", in cui i risultati prodotti dal modello vengono confrontati con quelli ottenuti dal DNS. A direct numerical simulation (DNS) is a simulation in computational fluid dynamics (CFD) in which the Navier–Stokes equations are numerically solved without any turbulence model. This means that the whole range of spatial and temporal scales of the turbulence must be resolved. All the spatial scales of the turbulence must be resolved in the computational mesh, from the smallest dissipative scales (Kolmogorov microscales), up to the integral scale , associated with the motions containing most of the kinetic energy. The Kolmogorov scale, , is given by where is the kinematic viscosity and is the rate of kinetic energy dissipation. On the other hand, the integral scale depends usually on the spatial scale of the boundary conditions. To satisfy these resolution requirements, the number of points along a given mesh direction with increments , must be so that the integral scale is contained within the computational domain, and also so that the Kolmogorov scale can be resolved. Since where is the root mean square (RMS) of the velocity, the previous relations imply that a three-dimensional DNS requires a number of mesh points satisfying where is the turbulent Reynolds number: Hence, the memory storage requirement in a DNS grows very fast with the Reynolds number. In addition, given the very large memory necessary, the integration of the solution in time must be done by an explicit method. This means that in order to be accurate, the integration, for most discretization methods, must be done with a time step, , small enough such that a fluid particle moves only a fraction of the mesh spacing in each step. That is, ( is here the Courant number). The total time interval simulated is generally proportional to the turbulence time scale given by Combining these relations, and the fact that must be of the order of , the number of time-integration steps must be proportional to . By other hand, from the definitions for , and given above, it follows that and consequently, the number of time steps grows also as a power law of the Reynolds number. One can estimate that the number of floating-point operations required to complete the simulation is proportional to the number of mesh points and the number of time steps, and in conclusion, the number of operations grows as . Therefore, the computational cost of DNS is very high, even at low Reynolds numbers. For the Reynolds numbers encountered in most industrial applications, the computational resources required by a DNS would exceed the capacity of the most powerful computers currently available. However, direct numerical simulation is a useful tool in fundamental research in turbulence. Using DNS it is possible to perform "numerical experiments", and extract from them information difficult or impossible to obtain in the laboratory, allowing a better understanding of the physics of turbulence. Also, direct numerical simulations are useful in the development of turbulence models for practical applications, such as sub-grid scale models for large eddy simulation (LES) and models for methods that solve the Reynolds-averaged Navier–Stokes equations (RANS). This is done by means of "a priori" tests, in which the input data for the model is taken from a DNS simulation, or by "a posteriori" tests, in which the results produced by the model are compared with those obtained by DNS. En analys med metoden Direkt Numerisk Simulering (Direct numerical simulation, DNS) är en simulering med CFD-teknik där Navier–Stokes ekvationer löses numeriskt utan att använda någon turbulensmodell. Unter Direkter Numerischer Simulation, kurz DNS, versteht man eine Berechnungsmethode der Strömungsmechanik zur rechnerischen Lösung der vollständigen instationären Navier-Stokes-Gleichungen. Sie unterscheidet sich von anderen Berechnungsmethoden der Strömungsmechanik dadurch, dass kleinskalige turbulente Schwankungen numerisch in Raum und Zeit aufgelöst und nicht durch Turbulenzmodelle dargestellt werden. Aufgrund der zeitlich variierenden, räumlich kleinen Schwankungen in einer turbulenten Strömung ist neben der hohen räumlichen Auflösung eine instationäre Betrachtungsweise für die detaillierte Beschreibung der physikalischen Vorgänge erforderlich. Die DNS ist damit die genaueste Methode, Strömungen zu berechnen; sie stellt allerdings auch die höchsten Anforderungen an das numerische Verfahren sowie an die zur Verfügung stehende Rechenleistung. Deshalb findet die DNS hauptsächlich in der Grundlagenforschung Verwendung. Ein großer Anwendungsbereich ist der laminar-turbulente Umschlag, unter dem man den Übergang von einer glatten stationären Strömung in den quasichaotischen turbulenten Zustand versteht. Des Weiteren wird die DNS in den Bereichen Ablöseblasen, vollturbulente Strömungen und Aeroakustik eingesetzt und dient auch der Weiterentwicklung von Turbulenzmodellen.

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